given the ellispe list a,b,c,d

Mathematics
Tutor: None Selected Time limit: 1 Day

Aug 28th, 2015

Hello!

Again, make this equation to canonical form, for this completing squares:

8x^2 + 80x = 8*(x^2 + 10) = 8*((x+5)^2 - 25) = 8*(x+5)^2 - 200,
y^2 - 6y = (y-3)^2 - 9.

So, the equation becames

8*(x+5)^2 - 200 + (y-3)^2 - 9 + 193 = 0, or
8*(x+5)^2 + (y-3)^2 = 200 + 9 - 193 = 16.

Now divide both sides by 16 and obtain

(x+5)^2/2 + (y-3)^2/16 = 1.

Therefore the answers are:

a. (-5,3)
b. 2*sqrt(16) = 8
c. 2*sqrt(2)
d. sqrt(16-2) = sqrt(14)

Please ask if anything is unclear.
Aug 28th, 2015

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