Question

x² + y² - 8x + 2y + 1 = 0 is the equation of a circle with center (h, k) and radius r for: h = and k = and r = graph the circle.

Explanation:

Step1: Complete the square for \(x\) terms

Group \(x\) terms: \(x^{2}-8x=(x - 4)^{2}-16\).

Step2: Complete the square for \(y\) terms

Group \(y\) terms: \(y^{2}+2y=(y + 1)^{2}-1\).

Step3: Rewrite the equation

The original equation \(x^{2}+y^{2}-8x + 2y+1 = 0\) becomes \((x - 4)^{2}-16+(y + 1)^{2}-1+1 = 0\).
Simplify to \((x - 4)^{2}+(y + 1)^{2}=16\).

Answer:

\(h = 4\), \(k=-1\), \(r = 4\)