JEE Main 2021 (Online) 20th July Morning Shift | Conic Sections Question 96 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2021 (Online) 20th July Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let the tangent to the parabola S : y² = 2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the point R. Then the area (in sq. units) of the triangle PQR is equal to :

A

$${{25} \over 2}$$

B

$${{35} \over 2}$$

C

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

D

25

2

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

+4

-1

Consider a hyperbola H : x² $$-$$ 2y² = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁ > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :

A

$${\sqrt 6 }$$ $$-$$ 1

B

$${7 \over {\sqrt 6 }}$$ $$-$$ 2

C

$${4\sqrt 6 }$$ $$-$$ 1

D

$${4\sqrt 6 }$$

3

JEE Main 2021 (Online) 18th March Evening Shift

MCQ (Single Correct Answer)

+4

-1

Let a tangent be drawn to the ellipse $${{{x^2}} \over {27}} + {y^2} = 1$$ at $$(3\sqrt 3 \cos \theta ,\sin \theta )$$ where $$0 \in \left( {0,{\pi \over 2}} \right)$$. Then the value of $$\theta$$ such that the sum of intercepts on axes made by this tangent is minimum is equal to :

A

$${{\pi \over 6}}$$

B

$${{\pi \over 3}}$$

C

$${{\pi \over 8}}$$

D

$${{\pi \over 4}}$$

4

JEE Main 2021 (Online) 17th March Evening Shift

MCQ (Single Correct Answer)

+4

-1

Let L be a tangent line to the parabola y² = 4x $$-$$ 20 at (6, 2). If L is also a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$$, then the value of b is equal to:

A

20

B

14

C

16

D

11

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