Write the following in standard form and identify the conic section. 2x^2+ 7y^2 + 24x + 84y + 310 = 0

Question

I need step by step instructions to put this ellipse equation in standard form.

Answer 1

We have to complete two squares here, one for x and one for y. Begin by rewriting:

2[x² + 12x + ___ ] + 7[y² + 12y + ___ ] = -310. Now, we complete each square and balance:

2[x² + 12x + 36 ] + 7[y² + 12y + 36 ] = -310 + 72 + 252

2(x + 6)² + 7(y + 6)² = 14 Divide both sides by 14

(x + 6)² / 7 + (y + 6)² / 2 = 1 Is an ellipse oriented horizontally, centered at (-6 , -6), with a = √7 , b = √2 , c = √5