1
WB JEE 2024
+1
-0.25

With origin as a focus and $$x=4$$ as corresponding directrix, a family of ellipse are drawn. Then the locus of an end of minor axis is

A
a circle
B
a parabola
C
a straight line
D
a hyperbola
2
WB JEE 2023
+1
-0.25

The tangent at point $$(a\cos \theta ,b\sin \theta ),0 < \theta < {\pi \over 2}$$, to the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ meets the x-axis at T and y-axis at T$$_1$$. Then the value of $$\mathop {\min }\limits_{0 < \theta < {\pi \over 2}} (OT)(O{T_1})$$ is

A
ab
B
2ab
C
0
D
1
3
WB JEE 2023
+1
-0.25

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$, and an extremity of its minor axis is inclined at an angle 60$$^\circ$$, then the eccentricity of the ellipse is

A
$${{\sqrt 3 } \over 2}$$
B
$${1 \over 2}$$
C
$${{\sqrt 7 } \over 3}$$
D
$${1 \over {\sqrt 3 }}$$
4
WB JEE 2022
+1
-0.25

AB is a variable chord of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. If AB subtends a right angle at the origin O, then $${1 \over {O{A^2}}} + {1 \over {O{B^2}}}$$ equals to

A
$${1 \over {{a^2}}} + {1 \over {{b^2}}}$$
B
$${1 \over {{a^2}}} - {1 \over {{b^2}}}$$
C
$${a^2} + {b^2}$$
D
$${a^2} - {b^2}$$
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