Question

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

(a) 4

(b) 5

(c) 6

(d) 9

Answer 1

 Let equation of circle touching $x$-axis is

$x^2-2 h x+h^2+y^2-2 k y=0$

Since, it passes through $(2,2)$ and $(9,9)$

$\begin{array}{l}\therefore \quad 4-4 h+h^2+4-4 k=0 \\\text { and } \quad 81-18 h+81+h^2-18 k=0 \\\end{array}$

On solving, we get $h=6$

So, The correct option of this question will be (C).