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

Step-by-step solution

The given information can be represented in the form of the diagram below.​​​​​ Since angle in a semicircle is a right angle. Hence, the other circle will be passing through the centre of the first circle. The two ends of diameter of the circle is O 0 , 0   and   C 3 , - 2 . Hence, the required equation of circle is x - 0 x - 3 + y - 0 y - - 2 = 0 ⇒ x 2 + y 2 - 3 x + 2 y = 0 Put α , 1 2 in the above equation ⇒ α 2 + 1 4 - 3 α + 1 = 0 ⇒ α 2 - 3 α + 5 4 = 0 ⇒