1
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
$${\pi \over 6}$$
2
WB JEE 2019
+1
-0.25
S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is
A
$${1 \over 4}$$
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$${2 \over 3}$$
3
WB JEE 2019
+1
-0.25
P is the extremity of the latusrectum of ellipse $$3{x^2} + 4{y^2} = 48$$ in the first quadrant. The eccentric angle of P is
A
$${\pi \over 8}$$
B
$${{3\pi } \over 4}$$
C
$${\pi \over 3}$$
D
$${{2\pi } \over 3}$$
4
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
$${{9{x^2}} \over {49}} + {{{y^2}} \over 9} = 1$$
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