Question

What is the equation of the circle whose has endpoints (9,1) and (9,15)

Answer 1

step 1

Find the center of the circle

we have that

the center of the circle is the midpoint between the endpoints

sp

$\begin{gathered} M(\frac{9+9}{2},\frac{1+15}{2}) \\ M(9,8) \end{gathered}$

step 2

Find the radius of the circle

we have that

the distance between endpoints is equal to the diameter of circle

so

D=15-1=14 units -------> (difference of the y-coordinates)

Remember that the radius is half the diameter

r=D/2

r=14/2=7 units

step 3

Find the equation of the circle

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

where

*h,k) is the center

r is the radius

substitute

(x-9)^2+(y-8)^2=7^2

(x-9)^2+(y-8)^2=49