Find the coordinates of the center of a circle that is graph

Find the coordinates of the center of a circle that is graphed tangent to the x-axis and intersects the y-axis at (0, 9) and (0, 25).

Solution

Solution:

SInce x axis is tangent to the circle

thus assume the co-orditnates of center is (h,k) where

Now

we know that equation of circle

(x-h)² + (y-k)² = r²

h and k are co-ordinate of center and r is radius

Plug (0, 9) because it satisfy above equation

(0-h)² +(9-k)²= r²

and (0,25)

(0-h)² +(25-k)²= r²

from above

we can find the value of h , k

k = 17

h= 0

therefore co-ordinates of the center = (0 ,17)

answer