First slide

Definition of a circle

Question

The points on the line x = 2 from which the tangents drawn to the circle $x^{2} + y^{2} = 16$ are at right angles is (are)

Moderate

A

$(2, 2 \sqrt{7})$
B

$(2, 2 \sqrt{5})$
C

$(2, - 2 \sqrt{7})$
D

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

Solution

The point from which the tangents drawn are at right angle lies on the director circle.
Equation of director circle $x^{2} + y^{2} = 2 \times 16 = 32$ .
Putting x = 2, we get
y² = 28
or $y = \pm 2 \sqrt{7}$
So, the points can be $(2, 2 \sqrt{7}) or (2, - 2 \sqrt{7})$

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