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

A. (x - 2)^2 + (y + 3)^2 = 18.

B. (2, -3)

C. 3(2^(1/2))

Explanation:

The equation of this circle in standard form is (x - 2)^2 + (y + 3)^2 = 18. The center of the circle is at the point (2, -3), and its radius is 3(2^(1/2)) units.

Answer 2

• equation: (x -2)^2 +(y +3)^2 = 18
• center: (2, -3)
• radius: 3√2

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

__

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

(x, y) = (2, -3) . . . . . center

__

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

r = √18 = 3√2 . . . . . radius

_____

A graphing calculator can confirm these calculations.