The angle between a pair of tangents drawn from a point P t…

Maths Circle and System of Circles Mix Single Correct MCQ

Published on: August 14, 2026

The angle between a pair of tangents drawn from a point P to the circle x 2 + y 2 + 4x – 6y + 9 sin 2 α + 13 cos 2 α = 0 is 2 α .

The equation of the locus of the point P is -

x 2 + y 2 + 4x – 6y + 4 = 0

x 2 + y 2 + 4x – 6y – 9 = 0

x 2 + y 2 + 4x – 6y – 4 = 0

x 2 + y 2 + 4x – 6y + 9 = 0

Text Solution

Verified by Experts

The correct answer is:

The centre (–2, 3) and the radius is

= 2 sin α

Let (h, k) be a point from which tangents PA and PB are drawn to the given circle. Then as given ∠ CPA = ∠ CPB = α

Also, sin α = =

⇒ PC 2 = 4 (  AC = radius = 2 sin α )

⇒ (h + k) 2 + (k – 3) 2 = 4

or locus is x 2 + y 2 + 4x – 6y + 9 = 0 on replacing h and k by x and y.

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