JEE Main 2021 (Online) 27th July Morning Shift | Conic Sections Question 86 | Mathematics

JEE Main 2021 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)

-1

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $${1 \over 3}$$ and the distance of the nearer focus from this directrix is $${8 \over {\sqrt {53} }}$$, then the equation of the other directrix can be :

11x + 7y + 8 = 0 or 11x + 7y $$-$$ 15 = 0

11x $$-$$ 7y $$-$$ 8 = 0 or 11x + 7y + 15 = 0

2x $$-$$ 7y + 29 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0

2x $$-$$ 7y $$-$$ 39 = 0 or 2x $$-$$ 7y $$-$$ 7 = 0

JEE Main 2021 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)

-1

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :

{(4, 0), (0, 6)}

$$\{ (2 + 2\sqrt 2 ,3 - \sqrt 5 ),(2 - 2\sqrt 2 ,3 + \sqrt 5 )\} $$

$$\{ (2 + 2\sqrt 2 ,3 + \sqrt 5 ),(2 - 2\sqrt 2 ,3 - \sqrt 5 )\} $$

{($$-$$1, 5), (5, 1)}

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 :

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

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

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

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