JEE Main 2021 (Online) 27th August Morning Shift | Conic Sections Question 79 | Mathematics

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

A tangent and a normal are drawn at the point P(2, $$-$$4) on the parabola y² = 8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that AQBP is a square, then 2a + b is equal to :

$$-$$16

$$-$$18

$$-$$12

$$-$$20

JEE Main 2021 (Online) 27th August Morning Shift

MCQ (Single Correct Answer)

-1

If x² + 9y² $$-$$ 4x + 3 = 0, x, y $$\in$$ R, then x and y respectively lie in the intervals :

$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$

$$\left[ { - {1 \over 3},{1 \over 3}} \right]$$ and [1, 3]

[1, 3] and [1, 3]

[1, 3] and $$\left[ { - {1 \over 3},{1 \over 3}} \right]$$

JEE Main 2021 (Online) 26th August Evening Shift

MCQ (Single Correct Answer)

-1

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

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