1
WB JEE 2018
+1
-0.25
Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of the ellipse x2 + 9y2 = 9, then the ratio of a2 : b2 equals to
A
8 : 1
B
1 : 8
C
9 : 1
D
1 : 9
2
WB JEE 2018
+1
-0.25
Let P be a point on the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and the line through P parallel to the Y-axis meets the circle x2 + y2 = 9 at Q, where P, Q are on the same side of the X-axis. If R is a point on PQ such that $${{PR} \over {RQ}} = {1 \over 2}$$, then the locus of R is
A
$${{{x^2}} \over 9} + {{9{y^2}} \over {49}} = 1$$
B
$${{{x^2}} \over {49}} + {{{y^2}} \over 9} = 1$$
C
$${{{x^2}} \over 9} + {{{y^2}} \over {49}} = 1$$
D
$${{9{x^2}} \over {49}} + {{{y^2}} \over 9} = 1$$
3
WB JEE 2017
+1
-0.25
Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ on the line bx $$-$$ ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is
A
2ab
B
ab
C
$${{({a^2} + {b^2})} \over 2}$$
D
$${a \over b}$$
4
WB JEE 2017
+1
-0.25
B is an extremity of the minor axis of an ellipse whose foci are S and S'. If $$\angle SBS'$$ is a right angle, then the eccentricity of the ellipse is
A
$${1 \over 2}$$
B
$${1 \over {\sqrt 2 }}$$
C
$${2 \over 3}$$
D
$${1 \over 3}$$
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