JEE Main 2021 (Online) 26th August Evening Shift | Conic Sections Question 82 | Mathematics

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

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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) 26th August Morning Shift

MCQ (Single Correct Answer)

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On the ellipse $${{{x^2}} \over 8} + {{{y^2}} \over 4} = 1$$ let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2y = 0. Let S and S' be the foci of the ellipse and e be its eccentricity. If A is the area of the triangle SPS' then, the value of (5 $$-$$ e²). A is :

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

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