Question

The equation 2x² + 2y2 – 8x - 12y + 16 = 0 defines a circle.

which of these shows a correct step for determining the center and radius of this circle? choose all that are correct.
(2x2 – 8x + 16) + (2y2 – 12y + 36) = -16 + 36
(x - 4)2 + (y - 9)2 = 5
(x2 - 4x + 4) + (y2 – 6y + 9) = -8 +13
ox? + y2 - 4x - 6y = -16
(x - 2)2 + (y - 3)2 = 5

Answer 1

C, E

Explanation:

Here, we want to change the equation of a circle from general form to standard form. This is done by making the leading coefficients 1, completing the squares, and then rewriting the equation in standard form.

The leading coefficients of the given equation are 2, so we first want to divide by 2. This gives ...

x² +y² -4x -6y +8 = 0

Subtracting 8 puts us in better position to complete the squares.

x² +y² -4x -6y = -8

Now, we can add the squares of half the coefficients of the linear terms.

(x² -4x +4) +(y² -6x +9) = -8 +13 . . . . . . matches C

And we can simplify this to the standard form equation:

(x -2)² +(y -3)² = 5 . . . . . matches E