1
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola
$${{{x^2}} \over 4} - {{{y^2}} \over 2} = 1$$ at the point $$\left( {{x_1},{y_1}} \right)$$. Then $$x_1^2 + 5y_1^2$$ is equal to :
A
5
B
6
C
10
D
8
2
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
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
$${1 \over 2}\sqrt {{{11} \over 3}}$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
If one end of a focal chord AB of the parabola y2 = 8x is at $$A\left( {{1 \over 2}, - 2} \right)$$, then the equation of the tangent to it at B is :
A
2x – y – 24 = 0
B
x – 2y + 8 = 0
C
x + 2y + 8 = 0
D
2x + y – 24 = 0
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
If e1 and e2 are the eccentricities of the ellipse, $${{{x^2}} \over {18}} + {{{y^2}} \over 4} = 1$$ and the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ respectively and (e1, e2) is a point on the ellipse, 15x2 + 3y2 = k, then k is equal to :
A
17
B
16
C
15
D
14
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