JEE Main 2021 (Online) 25th July Evening Shift | Conic Sections Question 88 | Mathematics

JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

-1

If a tangent to the ellipse x² + 4y² = 4 meets the tangents at the extremities of it major axis at B and C, then the circle with BC as diameter passes through the point :

$$(\sqrt 3 ,0)$$

$$(\sqrt 2 ,0)$$

(1, 1)

($$-$$1, 1)

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-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 :

$$16{x^2} - 9{y^2} + 32x + 36y - 36 = 0$$

$$9{x^2} - 16{y^2} + 36x + 32y - 144 = 0$$

$$16{x^2} - 9{y^2} + 32x + 36y - 144 = 0$$

$$9{x^2} - 16{y^2} + 36x + 32y - 36 = 0$$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

Let a parabola b be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O(0, 0) to the parabola P which meet P at S and R, then the area (in sq. units) of $$\Delta$$SOR is equal to :

$$16\sqrt 2 $$

$$8\sqrt 2 $$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

Let an ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, $${a^2} > {b^2}$$, passes through $$\left( {\sqrt {{3 \over 2}} ,1} \right)$$ and has eccentricity $${1 \over {\sqrt 3 }}$$. If a circle, centered at focus F($$\alpha$$, 0), $$\alpha$$ > 0, of E and radius $${2 \over {\sqrt 3 }}$$, intersects E at two points P and Q, then PQ² is equal to :

$${8 \over 3}$$

$${4 \over 3}$$

$${{16} \over 3}$$

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