16x^2+4y^2-32x+16y-32=0 find the ellipse

Question

graph a ellipse

Answer 1

16x^2+4y^2-32x+16y-32=0

16x^2 - 32x + 4y^2 + 16y = 32

look at the x's first, divide by 16

x^2 - 2x + 1 complete the square

take half of -2, -1 now square it +1

(x - 1)^2 is first part

(x -1)^2 + 4y^2 + 16y = 32 + 1

add the 1 to both sides

4y^2 + 16y

y^2 + 4y divide by 4

complete the square

y^2 + 4y + 4

(y+2)^2

(x - 1)^2 + (y + 2) ^2 = 33 + 4

(x - 1)^2 + (y + 2) ^2 = 37