Question

3x² + 3y² - 30x - 18y + 27 = 0 is the equation of a circle with center (h, k) and radius r for h = and k = and r = question help: video written example

Explanation:

Step1: Divide the equation by 3

$$\begin{align*} \frac{3x^{2}+3y^{2}-30x - 18y+27}{3}&=\frac{0}{3}\\ x^{2}+y^{2}-10x - 6y + 9&=0 \end{align*}$$

Step2: Complete the square for x - terms

$$\begin{align*} x^{2}-10x&=(x - 5)^{2}-25 \end{align*}$$

Step3: Complete the square for y - terms

$$\begin{align*} y^{2}-6y&=(y - 3)^{2}-9 \end{align*}$$

Step4: Substitute into the equation

$$\begin{align*} (x - 5)^{2}-25+(y - 3)^{2}-9+9&=0\\ (x - 5)^{2}+(y - 3)^{2}&=25 \end{align*}$$

Answer:

$h = 5$, $k = 3$, $r = 5$