find the center and the radius of the circle: 5x^2 - 20x + 5y^2 +10y + 26 = 0

Question

find the radius and circle by completing the square

Answer 1

First, we should rewrite this equation in this format, (x – h)² + (y – k)² = r², where (h,k) is the center and r is the radius, by completing the square:

5x² - 20x + 5y² + 10y + 26 = 0

5x² - 20x + 5y² + 10y = -26 Move number to the other side of the equation

5(x² - 4x + y² + 2y) = -26

(x² - 4x) + (y² + 2y) = -26/5 Divide by common factor and group variables

Now add half of the coefficient for the x and y terms squared (i.e. (-4/2)² = 4 and (2/2)² = 1) to both sides of the equation:

(x² - 4x + 4) + (y² + 2y + 1) = -26/5 + 4 + 9

Now we can factor and simplify:

(x - 2)² + (y + 1)² = 7.8

Therefore the center is (2,-1) and radius is sqrt(7.8) = 2.8.