Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2, 3).

Explanation

Since the radius of the circle is 5 and its center lies on the x-axis, the equation of the circle is `(x-h)^(2)+y^(2)=25`.
It is given that the circle passes through the point (2,3). Therefore,
`(2-h)^(2)+3^(2)=25`
or `(2-h^(2))=16`
or `2-h=+-4`
If `2-h=4,` then `h=2`
If `2-h= -4` then `h=6`
Therefore , the equation of circle is `(x+2)^(2)+y^(2)=25` or `(x+6)^(2)+y^(2)=25`.
Hence, `x^(2)+y^(2)+4x-21=0` or `x^(2)+y^(2)-12x+11=0`