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

7x^2 -28x + 7y^2 +42x = 35

divide by 7

x^2 -4x + y^2 + 6x = 5

complete the squares

x^2 -4x + 4 + y^2 +6x + 9 = 5 +4 + 9

(x-2)^2 + (y+3)^2 = 18 = (3sqr2)^2

circle's center is (2,-3) radius = 3sqr2 = about 4.2

Answer 2

7x^2 -28x + 7y^2 +42x = 35

divide by 7

x^2 -4x + y^2 + 6x = 5

complete the squares

x^2 -4x + 4 + y^2 +6x + 9 = 5 +4 + 9

(x-2)^2 + (y+3)^2 = 18 = (3sqr2)^

circle's center is (2,-3) radius = 3sqr2 = about 4.2