JEE Main 2021 (Online) 26th August Morning Shift | Circle Question 80 | Mathematics

If a line along a chord of the circle 4x² + 4y² + 120x + 675 = 0, passes through the point ($$-$$30, 0) and is tangent to the parabola y² = 30x, then the length of this chord is :

5$${\sqrt 3 }$$

3$${\sqrt 5 }$$

JEE Main 2021 (Online) 27th July Evening Shift

MCQ (Single Correct Answer)

-1

Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept $$6\sqrt 5 $$ on the x-axis. Then the radius of the circle C is equal to :

$$\sqrt {53} $$

$$\sqrt {82} $$

JEE Main 2021 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Two tangents are drawn from the point P($$-$$1, 1) to the circle x² + y² $$-$$ 2x $$-$$ 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :

$$(3\sqrt 2 + 2)$$

$$3(\sqrt 2 - 1)$$

JEE Main 2021 (Online) 27th July Morning Shift

MCQ (Single Correct Answer)

-1

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :

{(4, 0), (0, 6)}

$$\{ (2 + 2\sqrt 2 ,3 - \sqrt 5 ),(2 - 2\sqrt 2 ,3 + \sqrt 5 )\} $$

$$\{ (2 + 2\sqrt 2 ,3 + \sqrt 5 ),(2 - 2\sqrt 2 ,3 - \sqrt 5 )\} $$

{($$-$$1, 5), (5, 1)}

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