Question

Write an equation of the circle that passes through (2, 8) with center (-3 4)

Answer 1

we have, the equation is of the form

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

then, first calculate the radius of the circle

`\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)} \\ r=\sqrt[]{(14-14)^2+(-8-1)^2} \\ r=\sqrt[]{0+(-9)^2} \\ r=\sqrt[]{81} \\ r=9 \end{gathered}`

so, (h,k) is the center and the equation is

`\begin{gathered} (x-14)^2+(y-(-8))^2=9^2 \\ (x-14)^2+(y+8)^2=81 \end{gathered}`