NCERT Solutions for Class 11 Maths Maths Chapter 11

Conic Sections Class 11

Chapter 11 Conic Sections Exercise 11.1, 11.2, 11.3, 11.4, miscellaneous Solutions

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Exercise 11.1 : Solutions of Questions on Page Number : 241

Q1 :  

Find the equation of the circle with centre (0, 2) and radius 2


Answer :

The equation of a circle with centre (h, k) and radius r is given as

( - h)2 + (y ­- k)2 = r2

It is given that centre (h, k) = (0, 2) and radius (r) = 2.

Therefore, the equation of the circle is

(x - 0)2 + (y - 2)2 = 22

x2 + y2 + 4 ­- 4 y = 4

x2 + y2 ­- 4y = 0

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Q2 :  

Find the equation of the circle with centre (-2, 3) and radius 4


Answer :

The equation of a circle with centre (h, k) and radius r is given as

( - h)2 + (y ­- k)2 = r2

It is given that centre (h, k) = (-2, 3) and radius (r) = 4.

Therefore, the equation of the circle is

(x + 2)2 + (y - 3)2 = (4)2

x2 + 4x + 4 + y2 - 6y + 9 = 16

x2 + y2 + 4x - 6y - 3 = 0

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Q3 :  

Find the equation of the circle with centreand radius


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Q4 :  

Find the equation of the circle with centre (1, 1) and radius


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Q5 :  

Find the equation of the circle with centre (–a, –b) and radius


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Q6 :  

Find the centre and radius of the circle (x + 5)2 + (y - 3)2 = 36


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Q7 :  

Find the centre and radius of the circle x2 + y2 - 4x - 8y - 45 = 0


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Q8 :  

Find the centre and radius of the circle x2 + y2 - 8x + 10y - 12 = 0


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Q9 :  

Find the centre and radius of the circle 2x2 + 2y2 - x = 0


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Q10 :  

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x + y = 16.


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Q11 :  

Find the equation of the circle passing through the points (2, 3) and (-1, 1) and whose centre is on the line x - 3y - 11 = 0.


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Q12 :  

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2, 3).


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Q13 :  

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.


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Q14 :  

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).


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Q15 :  

Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?


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<< Previous Chapter 10 : Straight Lines Next Chapter 12 : Introduction to Three Dimensional Geometry >>

Exercise 11.2 : Solutions of Questions on Page Number : 246

Q1 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 12x


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Q2 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = 6y


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Q3 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = - 8x


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Q4 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = - 16y


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Q5 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 10x


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Q6 :  

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = -9y


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Q7 :  

Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = -6


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Q8 :  

Find the equation of the parabola that satisfies the following conditions: Focus (0, -3); directrix y = 3


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Q9 :  

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)


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Q10 :  

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (-2, 0)


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Q11 :  

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis


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Q12 :  

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis


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<< Previous Chapter 10 : Straight Lines Next Chapter 12 : Introduction to Three Dimensional Geometry >>

Exercise 11.3 : Solutions of Questions on Page Number : 255

Q1 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q2 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q3 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q4 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q5 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q6 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse


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Q7 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 36x2 + 4y2 = 144


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Q8 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 16x2 + y2 = 16


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Q9 :  

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse 4x2 + 9y2 = 36


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Q10 :  

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)


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Q11 :  

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)


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Q12 :  

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)


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Q13 :  

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)


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Q14 :  

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis, ends of minor axis ( ±1, 0)


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Q15 :  

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)


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Q16 :  

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)


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Q17 :  

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4


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Q18 :  

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.


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Q19 :  

Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).


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Q20 :  

Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2).


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<< Previous Chapter 10 : Straight Lines Next Chapter 12 : Introduction to Three Dimensional Geometry >>

Exercise 11.4 : Solutions of Questions on Page Number : 262

Q1 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola


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Q2 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola


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Q3 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y2 - 4x2 = 36


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Q4 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 - 9y2 = 576


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Q5 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y2 - 9x2 = 36


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Q6 :  

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 - 16x2 = 784


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Q7 :  

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)


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Q8 :  

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)


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Q9 :  

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)


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Q10 :  

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.


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Q11 :  

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.


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Q12 :  

Find the equation of the hyperbola satisfying the give conditions: Foci, the latus rectum is of length 8.


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Q13 :  

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12


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Q14 :  

Find the equation of the hyperbola satisfying the give conditions: Vertices ( ±7, 0),


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Q15 :  

Find the equation of the hyperbola satisfying the give conditions: Foci, passing through (2, 3)


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<< Previous Chapter 10 : Straight Lines Next Chapter 12 : Introduction to Three Dimensional Geometry >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 264

Q1 :  

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.


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Q2 :  

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.


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Q3 :  

An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?


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Q4 :  

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.


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Q5 :  

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.


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Q6 :  

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.


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Q7 :  

Find the area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the ends of its latus rectum.


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Q8 :  

A man running a racecourse notes that the sum of the distances from the two flag posts form him is always 10 m and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.


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Q9 :  

An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.


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<< Previous Chapter 10 : Straight Lines Next Chapter 12 : Introduction to Three Dimensional Geometry >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Conic Sections ( Exercise 11.1, 11.2, 11.3, 11.4, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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