1
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
Out of Syllabus
If the line y = mx + c is a common tangent to the hyperbola
$${{{x^2}} \over {100}} - {{{y^2}} \over {64}} = 1$$ and the circle x2 + y2 = 36, then which one of the following is true?
A
5m = 4
B
8m + 5 = 0
C
c2 = 369
D
4c2 = 369
2
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Out of Syllabus
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
$$\left( {{9 \over 2},3} \right)$$
3
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
$$\left( {{{20} \over 3},12} \right)$$
4
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
$$\left( {{1 \over {\sqrt 2 }},0} \right)$$
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