1
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
Out of Syllabus
Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is $${1 \over 2}$$. If P(1, $$\beta$$), $$\beta$$ > 0 is a point on this ellipse, then the equation of the normal to it at P is :
A
4x – 3y = 2
B
8x – 2y = 5
C
7x – 4y = 1
D
4x – 2y = 1
2
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,
$$\phi \left( t \right) = {5 \over {12}} + t - {t^2}$$, then a2 + b2 is equal to :
A
145
B
126
C
135
D
116
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Out of Syllabus
The length of the minor axis (along y-axis) of an ellipse in the standard form is $${4 \over {\sqrt 3 }}$$. If this ellipse touches the line, x + 6y = 8; then its eccentricity is :
A
$${1 \over 3}\sqrt {{{11} \over 3}}$$
B
$${1 \over 2}\sqrt {{5 \over 3}}$$
C
$$\sqrt {{5 \over 6}}$$
D
$${1 \over 2}\sqrt {{{11} \over 3}}$$
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Out of Syllabus
Let the line y = mx and the ellipse 2x2 + y2 = 1 intersect at a ponit P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at $$\left( { - {1 \over {3\sqrt 2 }},0} \right)$$ and (0, $$\beta$$), then $$\beta$$ is equal to :
A
$${{\sqrt 2 } \over 3}$$
B
$${2 \over 3}$$
C
$${{2\sqrt 2 } \over 3}$$
D
$${2 \over {\sqrt 3 }}$$
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