Question

Tangent to the circle x² + y² = 4 at any point on it in the first quadrant makes intercepts OA and OB on x and y axes respectively, O being the centre of the circle. Find the minimum value of (OA + OB).

Answer 1

Let AB be the tangent in the first quadrant to the circle x² + y² = 4 which make intercepts OA and OB on x and y axis respectively,

Let S = OA + OB  ...(i)

Let q be the angle made by OP with positive direction of x - axis.

∴ Coordinates of P = (2 cos θ, 2 sin θ)

Coordinates of A = (2 sec θ, 0)

Coordinates of A = (0,2 cosec θ)