Question

Find the center (h,k) and the radius (r) of the circle with the given equations:

1. 2(x-2)^2+2(y+5)^2=28

2. 4x^2+4y^2-12x+16y-5=0

Answer 1

#1 is easy. just read them out of the equation. Divide by 2 to make it easier.

#2: (4x^2 - 12x) + (4y^2 + 16y) = 5
or
4(x^2 - 3x) + 4(y^2 + 4y) = 5

(x^2 - 3x) + (y^2 - 4y) = 5/4

Now, you need to make the parenthesized terms perfect squares by adding extra constants on both sides of the equation:

(x^2 - 3x + 9/4) + (y^2 - 4y + 4) = 5/4 + 9/4 + 4

(x - 3/2)^2 + (y - 2)^2 = 15/2

now you can read off h,k r^2 from that

Answer 2

8,9), x + 2y = 7 please solve this for me