1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let an ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$, passes through $$\left( {\sqrt {{3 \over 2}} ,1} \right)$$ and has eccentricity $${1 \over {\sqrt 3 }}$$. If a circle, centered at focus F($$\alpha$$, 0), $$\alpha$$ > 0, of E and radius $${2 \over {\sqrt 3 }}$$, intersects E at two points P and Q, then PQ2 is equal to :
A
$${8 \over 3}$$
B
$${4 \over 3}$$
C
$${{16} \over 3}$$
D
3
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Let $${E_1}:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,a > b$$. Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2 are the end points of minor axis of E1. If E1 and E2 have same eccentricities, then its value is :
A
$${{ - 1 + \sqrt 5 } \over 2}$$
B
$${{ - 1 + \sqrt 8 } \over 2}$$
C
$${{ - 1 + \sqrt 3 } \over 2}$$
D
$${{ - 1 + \sqrt 6 } \over 2}$$
3
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Out of Syllabus
Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :
A
$${{\pi \over 6}}$$
B
$${{\pi \over 3}}$$
C
$${{\pi \over 8}}$$
D
$${{\pi \over 4}}$$
4
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Out of Syllabus
If the points of intersections of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$$ and the
circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :
A
12
B
10
C
6
D
5
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