1
WB JEE 2020
+1
-0.25
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OPQ$$ is equilateral, O being the centre of the hyperbola. Then the eccentricity e satisfies the relation
A
$$1 < e < {2 \over {\sqrt 3 }}$$
B
$$e = {2 \over {\sqrt 3 }}$$
C
$$e = {{\sqrt 3 } \over 2}$$
D
$$e > {2 \over {\sqrt 3 }}$$
2
WB JEE 2020
+1
-0.25
If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over 9} = 1$$, then the area of the rhombus SBS' B' will be
A
12 sq units
B
48 sq units
C
24 sq units
D
36 sq units
3
WB JEE 2020
+2
-0.5
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
A
$${\pi \over 4}$$
B
$${\pi \over 3}$$
C
$${\pi \over 2}$$
D
$${\pi \over 6}$$
4
WB JEE 2020
+2
-0.5
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of the curve intercepted between the point of contact and the directrix subtends at the corresponding focus an angle of
A
$${\pi \over 4}$$
B
$${\pi \over 3}$$
C
$${\pi \over 2}$$
D
$${\pi \over 6}$$
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