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
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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)
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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)
e g a P
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)
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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
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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
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(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 .
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20. i)
2
x y 1
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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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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
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