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The circle passing through $(1,-2)$ and touching the axis of x at $(3,0)$ also passes through the point.

$\begin{array}{1 1}(A)\;(-5,2) \\(B)\;(2,-5) \\(C)\;(5,-2) \\(D)\;(-2,5) \end{array}$

Can you answer this question?

Since circle touches x-axis at $(3,0)$
The equation of circle be
$(x-3)^2+(y-0)^2+\lambda y=0$
As it passes through $(1,-2)$
Put $x=1 ; y=-2$
=> $(1-3)^2+(-2)^2+\lambda(-2)=0$
$\lambda=4$
equation of circle is
$(x-3)^2+y^{-8}=0$
Now, from the option $(5,-2)$ satisfies equation of circle.
Hence C is the correct answer.
answered Apr 9, 2014 by