1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
Out of Syllabus
Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x2 $$-$$ y2 = 3. If L is also a tangent to the parabola y2 = $$\alpha$$x, then $$\alpha$$ is equal to :
A
12
B
$$-$$12
C
24
D
$$-$$24
2
JEE Main 2021 (Online) 18th March Evening Shift
+4
-1
Out of Syllabus
Consider a hyperbola H : x2 $$-$$ 2y2 = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x1, y1), x1 > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :
A
$${\sqrt 6 }$$ $$-$$ 1
B
$${7 \over {\sqrt 6 }}$$ $$-$$ 2
C
$${4\sqrt 6 }$$ $$-$$ 1
D
$${4\sqrt 6 }$$
3
JEE Main 2021 (Online) 16th March Morning Shift
+4
-1
The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over {16}} = 1$$ is :
A
(x2 + y2)2 $$-$$ 9x2 + 16y2 = 0
B
(x2 + y2)2 $$-$$ 9x2 + 144y2 = 0
C
(x2 + y2)2 $$-$$ 16x2 + 9y2 = 0
D
(x2 + y2)2 $$-$$ 9x2 $$-$$ 16y2 = 0
4
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
A hyperbola passes through the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is :
A
$${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$
B
$${{{x^2}} \over 9} - {{{y^2}} \over 16} = 1$$
C
$${{{x^2}} \over 9} - {{{y^2}} \over 25} = 1$$
D
x2 $$-$$ y2 = 9
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