jee-main 2023 Q70

jee-main · India · session2_08apr_shift2 Circles Inscribed/Circumscribed Circle Computations

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 $\left( \alpha , \frac { 1 } { 2 } \right)$, then a value of $\alpha$ is
(1) $\frac { 3 } { 2 }$
(2) $- \frac { 1 } { 2 }$
(3) $\frac { 5 } { 2 }$
(4) 1

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 $\left( \alpha , \frac { 1 } { 2 } \right)$, then a value of $\alpha$ is\\
(1) $\frac { 3 } { 2 }$\\
(2) $- \frac { 1 } { 2 }$\\
(3) $\frac { 5 } { 2 }$\\
(4) 1

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