JEE Main 2019 (Online) 9th January Evening Slot | Parabola Question 99 | Mathematics

Let A(4, $$-$$ 4) and B(9, 6) be points on the parabola, y² = 4x. Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of $$\Delta $$ACB is maximum. Then, the area (in sq. units) of $$\Delta $$ACB, is :

$$31{1 \over 4}$$

$$30{1 \over 2}$$

$$31{3 \over 4}$$

JEE Main 2019 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-1

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

(5, 2$$\sqrt 6$$)

(6, 4$$\sqrt 2$$)

(8, 6)

(4, -4)

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MCQ (Single Correct Answer)

-1

Out of Syllabus

Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x is :

$$2\sqrt 3 $$y = 12x + 1

$$\sqrt 3 $$y = x + 3

$$2\sqrt 3 $$y = -x - 12

$$\sqrt 3 $$y = 3x + 1

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MCQ (Single Correct Answer)

-1

If $$\theta $$ denotes the acute angle between the curves, y = 10 – x² and y = 2 + x² at a point of their intersection, the |tan $$\theta $$| is equal to :

$$8 \over 15$$

$$4 \over 9$$

$$7 \over 17$$

$$8 \over 17$$

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