CLASS : XIth SUBJECT : MATHS

DATE : Solutions DPP NO. : 7

Topic :- CONIC SECTION

1. The equation of the unit circle concentric with 𝑥2 + 𝑦2.8𝑥 + 4𝑦 ― 8 = 0 is

a) 𝑥2 + 𝑦2 ―8 𝑥 + 4 𝑦 ― 8 = 0
b) 𝑥2 + 𝑦2 ―8 𝑥 + 4 𝑦 + 8 = 0
c) 𝑥2 + 𝑦2 ―8 𝑥 + 4 𝑦 ― 28 = 0
d)𝑥2 + 𝑦2 ―8 𝑥 + 4 𝑦 + 19 = 0

2. If (9𝑎, 6𝑎) is a point bounded in region formed by parabola 𝑦2 = 16𝑥 and 𝑥 = 9, then
1
a) 𝑎 ∈ (0,1) b) 𝑎 < 4 c) 𝑎 < 1 d)0 < 𝑎 < 4

3. If the coordinates of the vertices of an ellipse are ( ― 6,1) and (4,1) and the equation of a focal
chord passing through the focus on the right side of the centre is 2𝑥 ― 𝑦 ― 5 = 0. The equation of
the ellipse is
(𝑥 + 1)2 (𝑦 + 1)2
a) 25
+ 16
=1
(𝑥 + 1)2 (𝑦 ― 1)2
b) 25 + 16
=1
(𝑥 ― 1)2 (𝑦 + 1)2
c) 25 + 16
=1
d)None of these

4. The radius of the circle 𝑟 = 3sin θ + cos θ is

a) 1 b) 2 c) 3 d)4

𝑥2 𝑦2 9
5. If the latusrectum of the hyperbola 16 ― 𝑏2 = 1 is 2, then its eccentricity is
a) 4/5 b) 5/4 c) 3/4 d)4/3

6. 𝑆 and 𝑇 are the foci of an ellipse and 𝐵 is end point of the minor axis . If 𝑆𝑇𝐵 is an equilateral
triangle, the eccentricity of the ellipse is
1 1 1 2
a) 4 b) 3 c) 2 d) 3

7. The eccentricity of the hyperbola can never be equal to

9 1 1
a) 5
b) 2 9
c) 3 8
d)2

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 𝑥2 𝑦2
8. If the tangent at (𝛼,𝛽) to the hyperbola 𝑎2 ― 𝑏2 = 1 cuts the auxiliary circle at points whose
1 1
ordinates are 𝑦1 and 𝑦2, then 𝑦1 + 𝑦2 =
1 2 1 2
a) 𝛼 b) 𝛼 c) 𝛽 d) 𝛽

1999
9. The eccentricity of the hyperbola 3
(𝑥2 ― 𝑦2) = 1, is
a) 2 b) 2 c) 2 2 d) 3

10. If the line 3𝑥 ― 4𝑦 ― 𝑘 = 0, (𝑘 > 0) touches the circle 𝑥2 + 𝑦2 ―4𝑥 ― 8𝑦 ― 5 = 0 at (𝑎, 𝑏), then
𝑘 + 𝑎 + 𝑏 is equal to
a) 20 b) 22 c) ―30 d) ―28

11. The length of the latusrectum of the parabola whose focus is (3,3) and directrix is
3𝑥 ― 4𝑦 ― 2 = 0, is
a) 2 b) 1 c) 4 d)None of these

12. The equation of the tangent from the point (0, 1) to the circle
𝑥2 + 𝑦2 ―2𝑥 ― 6𝑦 + 6 = 0, is
a) 𝑦 ― 1 = 0 b) 4𝑥 + 3𝑦 + 3 = 0 c) 4𝑥 ― 3𝑦 ― 3 = 0 d)𝑦 + 1 = 0

13. The circles 𝑥2 + 𝑦2 +6𝑥 + 6𝑦 = 0 and 𝑥2 + 𝑦2 ―12𝑥 ― 12𝑦 = 0

a) Cut orthogonally b) Touch each other internally
c) Intersect two points d)Touch each other externally

14. If tangents at 𝐴 and 𝐵 on the parabola 𝑦2 = 4𝑎𝑥 intersect at point 𝐶, then ordinates of 𝐴, 𝐶 and
𝐵 are
a) Always in AP b) Always in GP c) Always in HP d)None of these

15. The equations of the asymptotes of the hyperbola

2𝑥 +5𝑥𝑦 + 2𝑦2 ― 11𝑥 ― 7𝑦 ― 4 = 0 are
2

a) 2𝑥2 +5𝑥𝑦 + 2𝑦2 ― 11𝑥 ― 7𝑦 ― 5 = 0 b) 2𝑥2 +4𝑥𝑦 + 2𝑦2 ― 7𝑥 ― 11𝑦 + 5 = 0

c) 2𝑥2 +5𝑥𝑦 + 2𝑦2 ― 11𝑥 ― 7𝑦 + 5 = 0 d)None of the above

16. The circle 𝑥2 + 𝑦2 +2𝑔1𝑥 ― 𝑎2 = 0 and 𝑥2 + 𝑦2 +2𝑔2𝑥 ― 𝑎2 = 0 cut each other orthogonally. If
𝑝1,𝑝2 are perpendicular from (0, 𝑎) and (0, ― 𝑎) on a common tangent of these circles, then 𝑝1𝑝2 is
equal to
𝑎2
a) 2
b) 𝑎2 c) 2𝑎2 d)𝑎2 +2

17. If (𝑎cos α, 𝑏sin α), (𝑎cos β, 𝑏 sin β) are the end points of a focal chord of an ellipse 𝑏2𝑥2 + 𝑎2𝑦2
= 𝑎2𝑏2, then which of the following is correct?
α―β
sin α ― sin β cos ( )
a) 𝑒 = sin(α ― β) b) 𝑒 = 2
α+β
cos ( )
2
𝑒―1 α β
c) 𝑒 + 1 = tan tan d)None of these
2 2

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 18. A line meets the coordinates axes in 𝐴 and𝐵. A circle is circumscribed about the∆𝑂𝐴𝐵. The
distances from the points 𝐴 and 𝐵 of the side 𝐴𝐵 to the tangent at 𝑂 are equal to 𝑚 and 𝑛
respectively. Then, the diameter of the circle is
a) 𝑚(𝑚 + 𝑛) b) 𝑛(𝑚 + 𝑛) c) 𝑚 ― 𝑛 d)None of these

19. A line 𝐿 passing through the focus of the parabola (𝑦 ― 2)2 = 4(𝑥 + 1) intersects the parabola
in two distinct points. If m be the slope of the line 𝐿, then
a) 𝑚 ∈ ( ― 1,1)
b) 𝑚 ∈ ( ― ∞, ― 1) ∪ (1,∞)
c) 𝑚 ∈ ( ― ∞,0) ∪ (0,∞)
d)None of these

20. If 𝑎 > 2𝑏 > 0, then the positive value of 𝑚 fro which 𝑦 = 𝑚𝑥 ― 𝑏 1 + 𝑚2 is a common tangent
to 𝑥2 + 𝑦2 = 𝑏2 and (𝑥 ― 𝑎)2 + 𝑦2 = 𝑏2, is
2𝑏 𝑎2 ― 4𝑏2 2𝑏 𝑏
a) 𝑎2 ― 4𝑏2
b) c) 𝑎 ― 2𝑏 d) 𝑎 ― 2𝑏
2𝑏

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