Question

The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.

Answer 1

The standard equation for a circle is :

(x - h)² + (y - k) ² = r²

With center (h, k) and radius r

Lets write the given equation in this form.

Collect the like terms together :

7x² - 28x + 7y² + 42y = 35

Dividing through by 7 we have :

x² - 4x + y² + 6y = 5

Completing squares we have :

x² - 4x +(4/2)² + y² + 6y +(6/2)² = 5 + (4/2)² + (6/2)²

(x - 2)² + (y + 3)² = 5 + 4 + 9

(x - 2)² + (y + 3)² = 18

r² = 18

r = 4.243

Center : (2, - 3)