1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Let P(3, 3) be a point on the hyperbola,
$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :
A
$$\left( {{9 \over 2},2} \right)$$
B
$$\left( {{3 \over 2},2} \right)$$
C
(9,3)
D
$$\left( {{9 \over 2},3} \right)$$
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) 3rd September Evening Slot
+4
-1
Let the latus ractum of the parabola y2 = 4x be the common chord to the circles C1 and C2 each of them having radius 2$$\sqrt 5$$. Then, the distance between the centres of the circles C1 and C2 is :
A
8
B
12
C
$$8\sqrt 5$$
D
$$4\sqrt 5$$
4
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
$$\left( {{{20} \over 3},12} \right)$$
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