JEE Main 2019 (Online) 9th April Evening Slot | Conic Sections Question 152 | Mathematics

JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

If the tangent to the parabola y² = x at a point ($$\alpha $$, $$\beta $$), ($$\beta $$ > 0) is also a tangent to the ellipse, x² + 2y² = 1, then $$\alpha $$ is equal to :

$$\sqrt 2 + 1$$

$$\sqrt 2 - 1$$

$$2\sqrt 2 + 1$$

$$2\sqrt 2 - 1$$

JEE Main 2019 (Online) 9th April Evening Slot

MCQ (Single Correct Answer)

-1

The area (in sq. units) of the smaller of the two circles that touch the parabola, y² = 4x at the point (1, 2) and the x-axis is :-

$$4\pi \left( {3 +\sqrt 2 } \right)$$

$$8\pi \left( {2 - \sqrt 2 } \right)$$

$$8\pi \left( {3 - 2\sqrt 2 } \right)$$

$$4\pi \left( {2 - \sqrt 2 } \right)$$

JEE Main 2019 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

If the line y = mx + 7$$\sqrt 3 $$ is normal to the hyperbola $${{{x^2}} \over {24}} - {{{y^2}} \over {18}} = 1$$ , then a value of m is

$${3 \over {\sqrt 5 }}$$

$${{\sqrt 15 } \over 2}$$

$${{\sqrt 5 } \over 2}$$

$${2 \over {\sqrt 5 }}$$

JEE Main 2019 (Online) 9th April Morning Slot

MCQ (Single Correct Answer)

-1

If one end of a focal chord of the parabola, y² = 16x is at (1, 4), then the length of this focal chord is

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