1
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1
Out of Syllabus

The normal to the hyperbola

$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over 9} = 1$$ at the point $$\left( {8,3\sqrt 3 } \right)$$ on it passes through the point :

A
$$\left( {15, - 2\sqrt 3 } \right)$$
B
$$\left( {9,2\sqrt 3 } \right)$$
C
$$\left( { - 1,9\sqrt 3 } \right)$$
D
$$\left( { - 1,6\sqrt 3 } \right)$$
2
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
Out of Syllabus
The point $$P\left( { - 2\sqrt 6 ,\sqrt 3 } \right)$$ lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ having eccentricity $${{\sqrt 5 } \over 2}$$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point Q and R respectively, then QR is equal to :
A
$$4\sqrt 3$$
B
6
C
$$6\sqrt 3$$
D
$$3\sqrt 6$$
3
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The locus of the mid points of the chords of the hyperbola x2 $$-$$ y2 = 4, which touch the parabola y2 = 8x, is :
A
y3(x $$-$$ 2) = x2
B
x3(x $$-$$ 2) = y2
C
y2(x $$-$$ 2) = x3
D
x2(x $$-$$ 2) = y3
4
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
$$9{x^2} - 16{y^2} + 36x + 32y - 36 = 0$$
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