the equation of a circle is ______ what are the coordinates of the center and the length of the radius of this circle?

Question

equation- x²+y²-6y+1=0

Answer 1

Hi Savannah.

Here's how to do this one.

First, if it's a circle, we must rewrite the equation in the form: (x - h)² + (y - b)² = r²

where center is at (h, k) and the radius is r.

Given equation: x² + y² -6y + 1 = 0

x² + y² - 6y = -1 [subtracting 1 from each side

x² + (y - 6/2)² = -1 + (6/2)² [ The 6/2 is just half the coefficient of y

x² + (y - 3)² = -1 + 9

x² + (y - 3)² = 8 which is a circle, centered at (0, 3) and radius √8 = 2 √2