Suppose a circle passes through (2, 2) and (9, 9) and touches the $x$-axis at$P$. If $O$ is the origin, then $OP$ is equal to

Question

Dr. Abubacker · Accepted Answer

(c)
Let equation of circle touching $x$-axis is
$x^{2} - 2hx + h^{2} + y^{2} - 2ky = 0$
It passes through (2, 2) and (9, 9)
$\Rightarrow \ \ \ 4 - 4h + h^{2} + 4 - 4k = 0$ …(i)
and $81 - 18h + 81 + h^{2} - 18k = 0$ …(ii)
On solving Eqs. (i) and (ii), we get
$7h^{2} - 252 = 0\  \Rightarrow h = 6$

Q. Suppose a circle passes through (2, 2) and (9, 9) and touches the $x$-axis at$P$. If $O$ is the origin, then $OP$ is equal to

Explanation

Reviewed by Dr. Abubacker

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