Question

HELP! MEDALS WILL BE GIVEN I PROMISE!
What is the standard form of an ellipse?

Answer 1

i promise i will give medals.

Answer 2

You need to complete the squares on the LHS:

32x^2 - 256x + 9y^2 + 72y = -368
32(x^2 - 8x + _) + 9(y^2 + 8y + _) = -368 +32( _) + 9(_)

Note the factors on the RHS to keep the equation balanced
32(x^2 - 8x + 16) + 9(y^2 + 8y + 16) = -368 + 32(16) + 9(16)

(16 = (8/4)^2, the technique for completing the square)
32(x - 4)^2 + 9(y + 4)^2 = 288

now divide by 288 to put in standard form for ellipses:
(x - 4)^2 / 9 + (y + 4)^2 / 32 = 1

ellipse with center at (4,-4), vertical major axis

Answer 3

yaaaay thanls so much
medal coming