Question

complete the square and write the given equation in standard form. then give the center and radius of the circle and graph the equation.

$x^{2}-8x + y^{2}-9 = 0$

the equation in standard form is
(simplify your answer.)

Explanation:

Step1: Rearrange the equation

Group \(x\) - terms and \(y\) - terms: \((x^{2}-8x)+y^{2}=9\)

Step2: Complete the square for the \(x\) - terms

For \(x^{2}-8x\), use the formula \((a - b)^2=a^{2}-2ab + b^{2}\). Here \(a = x\) and \(2ab=8x\), so \(b = 4\). Then \(x^{2}-8x=(x - 4)^{2}-16\)
The equation becomes \((x - 4)^{2}-16+y^{2}=9\)

Step3: Write in standard form

Add \(16\) to both sides of the equation: \((x - 4)^{2}+y^{2}=9 + 16\)

Answer:

The standard form of the circle equation is \((x - 4)^{2}+y^{2}=25\)