Question

question 7
$2x^2 + 2y^2 + 20x + 4y + 34 = 0$ is the equation of a circle with center $(h, k)$ and radius $r$ for:
$h = \square$
and
$k = \square$
and
$r = \square$
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Explanation:

Step1: Divide the equation by 2

$$x^{2}+y^{2}+10x + 2y+17 = 0$$

Step2: Complete the square for x - terms

$$x^{2}+10x=(x + 5)^{2}-25$$

Step3: Complete the square for y - terms

$$y^{2}+2y=(y + 1)^{2}-1$$

Step4: Substitute into the equation

$$(x + 5)^{2}-25+(y + 1)^{2}-1+17 = 0$$
$$(x + 5)^{2}+(y + 1)^{2}-9 = 0$$
$$(x + 5)^{2}+(y + 1)^{2}=9$$

Answer:

\(h=-5\), \(k = - 1\), \(r = 3\)