Question

find the center and radius of the circle from the equation ( x^{2}+6x + y^{2}-2y - 39 = 0 ) center: radius: question help: message instructor submit question

Explanation:

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

Group \(x\) terms: \(x^{2}+6x=(x + 3)^{2}-9\)

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

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

Step3: Rewrite the equation

Substitute into original equation: \((x + 3)^{2}-9+(y - 1)^{2}-1-39 = 0\)
Simplify: \((x + 3)^{2}+(y - 1)^{2}=49\)

Answer:

Center: \((-3,1)\)
Radius: \(7\)