Help Ellipse Math?

Question

Can someone help me solve this quick?


4x^2 + y^2 - 8x + 4y + 4 = 0

i need to put this into ellipse equation form where x^2/a^2 + y^2/b^2 = 1

i put in the wrong equation. Im sorry. That one i already knew how to do.

This is the one
2x^2 + 4y^2 - 24x +56y + 260 =0

This one is hard. i cant do it.

Answer 1

Write the equation of the ellipse in standard form.

4x² + y² - 8x + 4y + 4 = 0
(4x² - 8x) + (y² + 4y) = -4
4(x² - 2x) + (y² + 4y) = -4
4(x² - 2x + 1) + (y² + 4y + 4) = -4 + 4*1 + 4
4(x - 1)² + (y + 2)² = 4
(x - 1)²/1 + (y + 2)²/4 = 1
____________________

This one works the same way.

2x² + 4y² - 24x + 56y + 260 = 0
x² + 2y² - 12x + 28y + 130 = 0
(x² - 12x) + (2y² + 28y) = -130
(x² - 12x) + 2(y² + 14y) = -130
(x² - 12x + 36) + 2(y² + 14y + 49) = -130 + 36 + 2*49
(x - 6)² + 2(y + 7)² = 4
(x - 6)²/4 + (y + 7)²/2 = 1