Question

A circle has its center at (0,0) and passes through the point (0,9). What is the standard equation of the circle?

Answer 1

x^2+y^2=9^2

Explanation:

The standard equation of a circle is:

`(x-h)^2+(y-k)^2=r^2`

Where the center of a circle is (h,k) and r is the radius of the circle. In this case because a circle is equidistant from the center and we have a point where it passes through 9 that means that the radius is 9. However, since the standard equation states that we must write r in the form of
`r^2` this means that
`r^2=9^2`. Therefore by plugging in the values we have:

`(x-0)^2+(y-0)^2=9^2\\\\x^2+y^2=9^2`