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Q.

Let O be the origin and OP and OQ be the tangents to the circles 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 $(α, \frac{1}{2})$ then a value of $α$ is

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a

3/2

b

1

c

5/2

d

-1/2

answer is B.

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Detailed Solution

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Question Image
Equation of circumcircle whose diametric equation point is (3, -2) and (0,0)
$x (x - 3) + y (y + 2) = 0 \Rightarrow x^{2} + y^{2} - 3 x + 2 y = 0$
$P (α, \frac{1}{2})$ is an circle
$\begin{array}{l} α^{2} - 3 λ + \frac{5}{4} = 0 \\ 4 α^{2} - 12 α + 4 = 0 \\ α = \frac{10}{4}, α = \frac{2}{4} \\ α = \frac{5}{2} or \frac{1}{2} \end{array}$

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