Question

write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). then graph the circle. r = 10; (h,k)=(-6,8) the standard form of the equation of this circle is (x + 6)^2+(y - 8)^2 = 100. the general form of the equation of this circle is (simplify your answer.)

Explanation:

Step1: Expand the standard - form equation

\[

$$\begin{align*} (x + 6)^2+(y - 8)^2&=100\\ (x + 6)(x + 6)+(y - 8)(y - 8)&=100\\ x^{2}+12x + 36+y^{2}-16y+64&=100 \end{align*}$$

\]

Step2: Simplify to get the general form

\[
x^{2}+y^{2}+12x-16y+36 + 64-100=0
\]
\[
x^{2}+y^{2}+12x-16y=0
\]

Answer:

\(x^{2}+y^{2}+12x - 16y=0\)