1
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $${1 \over 3}$$ and the distance of the nearer focus from this directrix is $${8 \over {\sqrt {53} }}$$, then the equation of the other directrix can be :
A
11x + 7y + 8 = 0 or 11x + 7y $$-$$ 15 = 0
B
11x $$-$$ 7y $$-$$ 8 = 0 or 11x + 7y + 15 = 0
C
2x $$-$$ 7y + 29 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
D
2x $$-$$ 7y $$-$$ 39 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0
2
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Out of Syllabus
If a tangent to the ellipse x2 + 4y2 = 4 meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through the point :
A
$$(\sqrt 3 ,0)$$
B
$$(\sqrt 2 ,0)$$
C
(1, 1)
D
($$-$$1, 1)
3
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
4
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
$${{ - 1 + \sqrt 6 } \over 2}$$
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