1
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
$${{ - 1 + \sqrt 6 } \over 2}$$
2
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
$${{\pi \over 4}}$$
3
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
4
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
A
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
B
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
C
$${\pi \over 2} - {\tan ^{ - 1}}\left( {{1 \over 3}} \right)$$
D
$${\pi \over 2} + {\tan ^{ - 1}}\left( {{1 \over 4}} \right)$$
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