Determine the equation of the circle with center left bracket, 3, comma, 9, right bracket(3,9) containing the point left bracket, 8, comma, minus, 3, right bracket(8,−3).
The equation of a circle with center (h,k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Given center (3, 9) and point (8, -3), we can find the radius by using the distance formula between the center and the point:
r = √((8 - 3)^2 + (-3 - 9)^2)
r = √(5^2 + (-12)^2)
r = √(25 + 144)
r = √169
r = 13
So, the equation of the circle is:
(x - 3)^2 + (y - 9)^2 = 169