Convert the following general form to standard form of an ellipse.4x²+9y²+48x+72y+144=0

Answer 1

You must use "completing the square" to get it into the proper "standard" format.

4x² + 9y² + 48x + 72y + 144 = 0

(4x² + 48x + ) + (9y² + 72y + ) = -144

4(x² + 12x + ) + 9(y² + 8y + ) = -144

4(x² + 12x + 36) + 9(y² + 8y + 16) = -144 + 4•36 + 9•16

4(x + 6)² + 9(y + 4)² = 144

4(x + 6)²/144 + 9(y + 4)²/144 = 144/144

(x + 6)²/36 + (y + 4)²/16 = 1 or with better formatting: