Question

Let O be the origin and OP and OQ be the tangents to the circle x² + y² - 6x + 4y + 8 = 0 at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point (α,1/2), then a value of α is.

(1) -1/2

(2) 5/2 

(3) 1 

(4) 3/2

Answer 1

Correct option is (2) 5/2 

Circumcircle of ΔOPQ 

(x – 0) (x–3) + (y–0) (y + 2) = 0 

x² + y² – 3x + 2y = 0

passes through \((\alpha,\frac{1}{2})\)