1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Out of Syllabus
On the ellipse $${{{x^2}} \over 8} + {{{y^2}} \over 4} = 1$$ let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 $$-$$ e2). A is :
A
6
B
12
C
14
D
24
2
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
3
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)
4
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
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