Question

Write the standard form of the equation of the circle described below. Center (0,-5) passes through the point (5,4)

Answer 1

Write the standard form of the equation of the circle described below. Center (0,-5) passes through the point (5,4)

step 1

Find the radius of the circle

Remember that the radius is the distance from the center to any point that lie in the circle

so

the radius is

$\begin{gathered} r=\sqrt[\square]{(4+5)^2+(5-0)^2} \\ r=\sqrt[\square]{106} \end{gathered}$

step 2

Find the equation of the circle in standard form

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

substitute

(x-0)^2+(y+5)^2=106

x^2+(y+5)^2=106