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 and its radius .

Step-by-step explanation:

You can put the equation into standard form by dividing by the leading coefficient, then completing the square for both x and y terms. It is useful to add 35 to eliminate the constant term from the left side.

  x^2 +y^2 -4x +6y = 5

Complete the square for x terms by adding (-4/2)^2 = 4.

  (x^2 -4x +4) +y^2 +6y = 9

Complete the square for y terms by adding (6/2)^2 = 9.

  (x -2)^2 +(y^2 +6y +9) = 18

  (x -2)^2 +(y +3)^2 = 18 . . . . . . . . . . standard form equation for the circle

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The coordinates of the center are the opposites of the constants in each squared binomial:

  (x, y) = (2, -3) . . . . . center

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The radius is the square root of the constant on the right:

  r = √18 = 3√2 . . . . . radius

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A graphing calculator can confirm these calculations.