Question

Rewrite the equation of this circle in standard form. Identify the center and radius.

Answer 1

Answer:

Center (3,13)

Radius r = 4

Step-by-step explanation:

Circle equation: $(x-h)^2 + (y-k)^2 = r^2$

Given: $y^2+x^2-6x-26y=-162$

Group x-term and y-term together:

$(x^2-6x) + (y^2-26y) = -162$

Complete the square for x-term, y-term using formula $"x^2+(2a)x+a^2 = (x+a)^2"$

$(x^2-(2)(3)x+(3)^2) + (y^2-(2)(13)y+(13)^2)=-162+(3)^2+(13)^2$

$(x-3)^2 + (y-13)^2=16$