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Consider a family of circles which are passing through the point $(-1,1)$ and are tangent to $x-$ axis. If $(h, k)$ are the co-ordinates of the centre of the circles, then the set of values of $k$ is given by the interval
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The correct answer is:
$k \geq 1 / 2$
$k \geq 1 / 2$
Equation of circle $(x-h)^2+(y-k)^2=k^2$
It is passing through $(-1,1)$ then
$\begin{aligned}
& (-1-h)^2+(1-k)^2=k^2 \\
& h^2+2 h-2 k+2=0 \\
& D \geq 0 \\
& 2 k-1 \geq 0 \Rightarrow k \geq 1 / 2.
\end{aligned}$
It is passing through $(-1,1)$ then
$\begin{aligned}
& (-1-h)^2+(1-k)^2=k^2 \\
& h^2+2 h-2 k+2=0 \\
& D \geq 0 \\
& 2 k-1 \geq 0 \Rightarrow k \geq 1 / 2.
\end{aligned}$
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