Untitled Document

Question Bank No: 1

1. The eccentricity of an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ whose latus rectum is half of its major axis is

a)		$\frac{1}{\sqrt{2}}$
b)		$\sqrt{\frac{2}{3}}$
c)		$\frac{\sqrt{3}}{2}$
d)		none of these

2. Sum of the focal distance of an ellipse $\frac{x^{2}}{a^{2}}$ + $\frac{y^{2}}{b^{2}}$ =1 is

a)		2b
b)		2a
c)		2ab
d)		a+b

3. The distance of a focus if the ellipse 9 $x^{2} + 16 y^{2} = 144$ from an end of the minor axis is

a)		$\frac{3}{2}$
b)		3
c)		4
d)		none of these

4. For the ellipse $\frac{x^{2}}{2} + \frac{y^{2}}{1} = 1$ the foci are

a)		( $\pm 1, 0)$
b)		(0, $\pm 1)$
c)		( $\pm \frac{1}{\sqrt{2}}, 0)$
d)		( $\pm \frac{1}{2}$ ,0)

5. The sum of distance of any point on the ellipse 3 $x^{2}$ +4 $y^{2} = 24$ from its foci is

a)		8 $\sqrt{2}$
b)		4 $\sqrt{2}$
c)		16 $\sqrt{2}$
d)		none of these

6. The latus rectum of the ellipse 5 $x^{2} + 9 y^{2}$ =45 is

a)		$\frac{10}{3}$
b)		$\frac{5}{3}$
c)		$\frac{5 \sqrt{5}}{3}$
d)		$\frac{10 \sqrt{5}}{3}$

7. The eccentricity of the conic 3 $x^{2} + 4 y^{2} = 24 is$

a)		$\frac{1}{4}$
b)		$\frac{7}{4}$
c)		$\frac{1}{2}$
d)		$\sqrt{\frac{7}{4}}$

8. The latus rectum of the conic 3 $x^{2}$ +4 $y^{2} - 6 x + 8 y - 5 = 0$ is

a)		3
b)		$\frac{\sqrt{3}}{2}$
c)		$\frac{2}{\sqrt{3}}$
d)		None of these

9. If S and $S^{'}$ are focus of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ =1 and P(x,y) be a point on it, then value of SP+ $S^{'} P$ is

a)		2b
b)		2a
c)		a-b
d)		a+b

10. The eccentricity of the curve represented by the equation $x^{2} + 2 y^{2} - 2 x + 3 y + 2 = 0$ is

a)		0
b)		$\frac{1}{2}$
c)		$\frac{1}{\sqrt{2}}$
d)		$\sqrt{2}$

11. The eccentricity of the ellipse $9 x^{2} + 5 y^{2} - 30 y = 0$ is

a)		$\frac{1}{3}$
b)		$\frac{2}{3}$
c)		$\frac{3}{4}$
d)		None of these

12. If the foci and the ends of the minor axis of an ellipse are the vertices of a square, the eccentricity is

a)		$\frac{1}{2}$
b)		$\frac{1}{3}$
c)		$\frac{1}{\sqrt{2}}$
d)		$\frac{1}{\sqrt{3}}$

13. The minor axis of the ellipse, whose axes are the coordinate axes with eccentricity $\frac{1}{3}$ and foci at $(\pm 2, 0)$ is

a)		4
b)		3
c)		8 $\sqrt{2}$
d)		4 $\sqrt{2}$

14. The major axis of the ellipse, whose axes are the coordinate axes with latus rectum 20, whose minor axis is the distance between the foci, is

a)		18
b)		20
c)		36
d)		40

15. The eccentricity of the ellipse whose axes are the coordinate axes and which passes through the points (2,2) and (3,1) is

a)		$\frac{1}{3}$
b)		$\sqrt{\frac{2}{3}}$
c)		$\frac{2}{5}$
d)		$\sqrt{\frac{2}{5}}$

16. The eccentricity of an ellipse, with centre at the origin, is $\frac{1}{2}$ . If one directrix is x=4, the equation of the ellipse is

a)		$3 x^{2} + 4 y^{2} = 1$
b)		$3 x^{2} + 4 y^{2} = 12$
c)		$4 x^{2} + 3 y^{2} = 1$
d)		$4 x^{2} + 3 y^{2} = 12$

17. On the ellipse 4 $x^{2} + 9 y^{2} = 1,$ the points at which the tangents are parallel to the line 8x=9y are

a)		$(\frac{2}{5}, \frac{1}{5})$
b)		$(- \frac{2}{5}, \frac{1}{5})$
c)		$(- \frac{2}{5}, - \frac{1}{5})$
d)		$(\frac{1}{5}, - \frac{1}{5})$

18. The number of values of c such that the straight line y=4x + c touches the curve $x^{2} + 4 y^{2} = 4$ is

a)		0
b)		1
c)		2
d)		infinite

19. If P=(x,y), $F_{1} = (3, 0), F_{2} = (- 3, 0)$ and 16 $x^{2} + 25 y^{2} = 400,$ then P $F_{1} + P F_{2} =$

a)		8
b)		6
c)		10
d)		12

20. If tangents are drawn to the ellipse $x^{2} + 2 y^{2} = 2$ then the locus of the midpoint of the intercept made by the tangents between the coordinate axes is

a)		$\frac{1}{2 x^{2}} + \frac{1}{4 y^{2}} = 1$
b)		$\frac{1}{4 x^{2}} + \frac{1}{2 y^{2}} = 1$
c)		$\frac{x^{2}}{2} + \frac{y^{2}}{4} = 1$
d)		$\frac{x^{2}}{4} + \frac{y^{2}}{2} = 1$

21. The value of $θ$ for which the sum of intercepts made by the tangent at $(3 \sqrt{3} \cos θ, \sin θ), 0 < θ < \frac{π}{2}$ to the ellipse $x^{2} + 27 y^{2} = 27$ on the coordinate exes is minimum is

a)		$\frac{π}{8}$
b)		$\frac{π}{6}$
c)		$\frac{π}{4}$
d)		$\frac{π}{3}$

22. The area of the quadrilateral formed by the tangents at the ends of latus-rectum of $5 x^{2} + 9 y^{2} = 45 is$

a)		27
b)		$\frac{27}{2}$
c)		$\frac{27}{4}$
d)		90