Consider the equation 4x^2 + 9y^2 - 64 + 72y + 364 = 0

[NEHA]

Consider the equation, 4x^2 + 9y^2 - 64 + 72y + 364 = 0. Tell what conic section this represents and sketch its graph.

This is what I did:

(4x^2 - 64x. . ..) + (9y^2 + 72. . . .) = -364
4(x^2 - 16x. . ..) + 9(y^2 + 8y. . . .) = -364
4(x^2 - 16x + 1) + 9(y^2 + 8y + 8 ) = -364 + __
4(x^2 - 16x + 1) + 9(y^2 + 8y + 8 ) = -364 + 4(1) + 9(8)
4(x^2 - 16x + 1) + 9(y^2 + 8y + 8 ) = -364 + 4 + 72
4(x - 1)^2 + 9(y + 0.9)^2 = -288

[4(x - 1)^2] / -288 + [9(y + 0.9)^2] / -288 = -288 / -288

or

(x - 1)^2 / (sqrt(-72))^2 + (y + 0.9)^2 / ((sqrt(-32)) = 1

Is this correct?

 

[tkhunny]

Re: Consider the equation

(4x^2 - 64x ) + (9y^2 + 72 ) = -364
4(x^2 - 16x ) + 9(y^2 + 8y ) = -364
4(x^2 - 16x + 1) + 9(y^2 + 8y + 8 ) = -36 + __

How did you decide on '1' and '8'?

For the 'x', 16/2 = 8, then 8^2 = 64
For the 'y', 8/2 = 4, then 4^2 = 16

Try those, instead.

How did -364 turn into -36?
Why did you switch to decimals and how did you pick 0.9?

You seem to have somewhat of a clue. Be MUCH more careful.