Question

Write the equation of the circle with center (3,2) and with (9,3) being a point on the circle

Answer 1

`(x-3)^2 + (y-2)^2 = 37`

Explanation:

To write the equation of a circle, use the formula
`(x-h)^2+(y-k)^2 = r^2` where the center of the circle is (h, k).

This means the equation is
`(x-3)^2 + (y-2)^2 = r^2`.

Find the radius r by finding the distance between (3,2) and (9,3) using the distance formula.

`d = √((9-3)^2 + (3-2)^2) =√(6^2 + 1^2) =√(36+1) =√(37)`

Since the radius is √37 and therefore
`r^2 = 37`.

The equation is
`(x-3)^2 + (y-2)^2 = 37`.