1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
For some $$\theta \in \left( {0,{\pi \over 2}} \right)$$, if the eccentricity of the
hyperbola, x2–y2sec2$$\theta$$ = 10 is $$\sqrt 5$$ times the
eccentricity of the ellipse, x2sec2$$\theta$$ + y2 = 5, then the length of the latus rectum of the ellipse, is :
A
$$\sqrt {30}$$
B
$$2\sqrt 6$$
C
$${{4\sqrt 5 } \over 3}$$
D
$${{2\sqrt 5 } \over 3}$$
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Out of Syllabus
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
3
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
4
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Out of Syllabus
If a hyperbola passes through the point P(10, 16) and it has vertices at (± 6, 0), then the equation of the normal to it at P is :
A
2x + 5y = 100
B
x + 3y = 58
C
x + 2y = 42
D
3x + 4y = 94
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