JEE Main 2022 (Online) 26th June Evening Shift | Hyperbola Question 32 | Mathematics

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 :

$$\left( {15, - 2\sqrt 3 } \right)$$

$$\left( {9,2\sqrt 3 } \right)$$

$$\left( { - 1,9\sqrt 3 } \right)$$

$$\left( { - 1,6\sqrt 3 } \right)$$

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-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 :

$$4\sqrt 3 $$

$$6\sqrt 3 $$

$$3\sqrt 6 $$

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

The locus of the mid points of the chords of the hyperbola x² $$-$$ y² = 4, which touch the parabola y² = 8x, is :

y³(x $$-$$ 2) = x²

x³(x $$-$$ 2) = y²

y²(x $$-$$ 2) = x³

x²(x $$-$$ 2) = y³

JEE Main 2021 (Online) 25th July Morning Shift