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

\[

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

\]

Step2: Combine like - terms and set equal to 0

\[

$$\begin{align*} x^2+12x + 36+y^2-16y + 64-100&=0\\ x^2+y^2+12x-16y&=0 \end{align*}$$

\]

Answer:

$x^{2}+y^{2}+12x - 16y=0$