1
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
Let e1 and e2 be the eccentricities of the ellipse,
$${{{x^2}} \over {25}} + {{{y^2}} \over {{b^2}}} = 1$$(b < 5) and the hyperbola,
$${{{x^2}} \over {16}} - {{{y^2}} \over {{b^2}}} = 1$$ respectively satisfying e1e2 = 1. If $$\alpha$$
and $$\beta$$ are the distances between the foci of the
ellipse and the foci of the hyperbola
respectively, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :
A
(8, 10)
B
(8, 12)
C
$$\left( {{{24} \over 5},10} \right)$$
D
$$\left( {{{20} \over 3},12} \right)$$
2
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
A hyperbola having the transverse axis of length $$\sqrt 2$$ has the same foci as that of the ellipse 3x2 + 4y2 = 12, then this hyperbola does not pass through which of the following points?
A
$$\left( {1, - {1 \over {\sqrt 2 }}} \right)$$
B
$$\left( {\sqrt {{3 \over 2}} ,{1 \over {\sqrt 2 }}} \right)$$
C
$$\left( { - \sqrt {{3 \over 2}} ,1} \right)$$
D
$$\left( {{1 \over {\sqrt 2 }},0} \right)$$
3
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
$${{2\sqrt 5 } \over 3}$$
4
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
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