Question

Analyze the equation of the ellipse: 4x^2+3y^2+16x-30y=-55

I got to here and I am stuck now.

4(x^2+4x)+3(y^2-10y)=-55

Answer 1

complete the square for each part

Answer 2

i'm noy sure of how to do that

Answer 3

\[4(x^2+4x+4)=3(y^2-10y+25)=-55+4\times 4+3\times 25\] is the first step

Answer 4

arithmetic on the right
the point of adding those numbers is now you can write
\[4(x+2)^2+3(x-5)^2=36\]

Answer 5

now divide by \(36\) and get
\[\frac{(x+2)^2}{9}+\frac{(y-5)^2}{12}=1\]

Answer 6

i see i made lots of typos, but the last line is correct
you know how to complete the square?

Answer 7

By dividing what was factored out ?

Answer 8

you mean the step from here \[4(x+2)^2+3(y-5)^2=36\] to here\[\frac{(x+2)^2}{9}+\frac{(y-5)^2}{12}=1\]?

Answer 9

yes

Answer 10

divided by 36 to get a 1 on the right and reduced to lowest terms

Answer 11

\[\frac{4}{36}=\frac{1}{9}\\
\frac{3}{36}=\frac{1}{12}\]

Answer 12

oh ok. I also have to find the center, vertices endpoints and foci. Do I use what you got at the end ?

Answer 13

yes