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

Answer:

x^2+y^2=9^2

Step-by-step 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:

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