Find the equation of circle which passes through point point (4,-2) which touches the axes such that the whole circle lies in fourth quadrant

For a circle that passes through a point(a,band touches both axes, the center of the circle lies on the perpendicular bisector of the line segment formed by the point and the origin.

Given the point (4, -2), the midpoint of the segment joining (4, -2) and the origin (0, 0) is $(ℎ,�)$, where $ℎ=\frac{4}{2}=2$ and $�=\frac{-2}{2}=-1$.

Now, the radius ($�$) is the distance from the center to the given point (4, -2). Using the distance formula:

$�=\sqrt{(4-2{)}^2+(-2-(-1){)}^2}=\sqrt{5}$

Therefore, the equation of the circle is:

$(�-2{)}^2+(�+1{)}^2=5$