Find the equation of the circle, centre (2, -3), which touches the x axis.
Please show all working out.
If the circle touches the x-axis, then the circle must pass through the point (2, 0). The distance from this point to the center (2, -3) is 3, so the radius is 3.
Thus,
$\displaystyle \begin{aligned}
(x - h)^2 + (y - k)^2 &= r^2 \\
(x - 2)^2 + (y - (-3))^2 &= 3^2 \\
(x - 2)^2 + (y + 3)^2 &= 9 \\
\end{aligned}$
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