1
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The locus of the centroid of the triangle formed by any point P on the hyperbola $$16{x^2} - 9{y^2} + 32x + 36y - 164 = 0$$, and its foci is :
A
$$16{x^2} - 9{y^2} + 32x + 36y - 36 = 0$$
B
$$9{x^2} - 16{y^2} + 36x + 32y - 144 = 0$$
C
$$16{x^2} - 9{y^2} + 32x + 36y - 144 = 0$$
D
$$9{x^2} - 16{y^2} + 36x + 32y - 36 = 0$$
2
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
3
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
$${4\sqrt 6 }$$
4
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
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