HSSlive-XI-Maths-Ch-11.CONIC SECTION.pdf

Remesh’s Mathematics 

[XI MATHEMATICS QUESTION BANK ] eccentricity and the length of the latus rectum of

CHAPTER 11

the ellipse 100 x

CONIC SECTION

2



2500 .

6. a) Directrix of the parabola parab ola

1. a) The length of latus rectum of the parabola parab ola  y

 25 y

(4)

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2

2

 x

2

 4ay

………… 

 8 x

.

(1)

(1)

i) -8

ii) 8

iii) -4

iv) 4

i)

 x  a 

iii)

0 

 y  a 

ii)

0 

iv)

 x  a 

0

 y  a 

0

 b) Find the equation of the ellipse ellipse whose whose length

 b) Find the coordinates coordinates of foci, the vertices, vertices, the

 0, 5  (3)

of the major axis is 20 and foci are

length of major axis, minor axis, the eccentricity and the latus rectum of the ellipse  x

2

25

is



y

IMPROVEMENT 2014

2

9

1

(3)

7. a) Which one of the following equations equations represents a parabola, which is symmetrical

MARCH 2017

about the positive y-axis?

2. a) Find the equation of of the parabola parab ola with focus (6,0) and equation of the directrix is  x  6 . (2)  b) Find the coordinates coordinates of the foci, foci, the vertices, vertices,

i)

iii)

eccentricity of the hyperbola

 x

16

 y



 8 x 2

 x 

 

4y



0 

2

 8 x

ii)

 y

iv)

 x  4 y 

2

0

are

 13,0  and foci are  5, 0  .

(3)

2

9

1

(3) MARCH 2014

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8. a) Consider the ellipse

3. Find the foci, vertices, the eccentricity and the length of the latus rectum of the hyperbola 2

2

 b) Find the equation of the ellipse ellipse whose whose vertices vertices

the length of transverse and conjugate axis and 2

 y

(1)

2

16 x  9 y  144 144  

 x

2

25

y



2

9

1.

Find the

coordinates of the foci, the length of major axis, the length of the minor axis, latus rectum

(4)

and eccentricity.

(4)

MARCH 2016

4. Find the foci, vertices , length of the major axis and eccentricity of the ellipse:

 x

2

25



y

2

9

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9. a) Find the centre and radius of the circle 1

 

(4)

SEPTEMBER 2015

2

2

 x  y  8 x  10 y  12 

0 . (2)  b) Determine Determine eccentricity eccentricity and length of latus latus

rectum of the hyperbola

5. Find the coordinates of the foci, vertices, Teaching Mathematics since 1990

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 x

2

16



y

    1

2

9

1

.

(2)

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Remesh’s Mathematics 

[XI MATHEMATICS QUESTION BANK ]

MARCH 2013

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

 x

2

25



y

2

9

 1.

(4)

a) The foci

(2)

 b) Eccentricity

(1)

c) Length of latus rectum.

(1)

MARCH 2010

16. An ellipse whose major axis as x-axis and the IMPROVEMENT 2012

centre (0,0) passes through (4,3) and ( 1,4).

11. Find the equation of the hyperbola where foci are

i)

 0, 8 

17. Consider the circle 12. A hyperbola whose transverse axis is x- axis,



(2)

IMPROVEMENT 2009

MARCH 2012

center (0,0) and the foci

(2)

ii) Find its eccentricity.

 and the length of the latus rectum is 24. (4)

Find the equation of the ellipse.

i)



2

2

 x  y  8 x  10 y  8 

(1)

Find the centre C and radius ‘r’.

ii) Find the equation of the circle with with centre at C

10,0   passes

and passing through the point (1,2).

through the point (3,2). a) Find the equation of the hyperbola.

(3)

 b) Find its eccentricity.

(1)

18. i)

(2)

Find the equation of the parabola with with vertex at (0,0) and focus at (0,2).

(1)

ii) Find the co-ordinates co-or dinates of the foci and the latus latus

IMPROVEMENT 2011

13. i)

0

rectum of the ellipse

Find the equation of the circle with centre (2,2) and passing through the point (2,5)

2

 x  16 y 

0.

2

25



y

2

9

 1.

(2)

(2) MARCH 2009

ii) Find the eccentricity eccentricity and the length of latus latus rectum of the parabola

 x

(2)

19. a) Find the center and radius of the circle 2

2

2 x  2 y  x  0  

MARCH 2011

(2)

 b) Find the equation of the parabola with with focus 14. i) Find the equation equation of the circle with center (2,2)

(6,0) and directrix

 x    6

 

(2)

and passing through the point (4,5). ii) Find the eccentricity eccentricity and the length of of latus rectum of the ellipse 4 x

2

 9y

2



36 .

MARCH 2008

20. i)

2





 x  y  1

IMPROVEMENT 2010

15. Consider the conic 9 y

The circle whose equation is

2

Teaching Mathematics since 1990

 4x

2



36 . Find

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2



2 has the centre

…….

(1)    2    e

ii) Find the equation of the tangent of the circle

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   g    a     P

Remesh’s Mathematics  2

 x  y



 13

[XI MATHEMATICS QUESTION BANK ]

at the point (2,3).

(2)

21. State whether the following is True or False: The line 2

 x  y

2

 x  y 

1

0  intersects the circle

in two points.

(1)

    3    e    g    a     P

Teaching Mathematics since 1990

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