Question

convert each equation to standard form by completing the square on x and y. Then graph the ellipse and give the location of its foci.

4x^2+25y^2-24x+100y+36=0

i need the steps

Answer 1

because i did the problem but i think i messed up

Answer 2

\[4x^2-24x+25y^2-100y=-36\]
\[4(x^2-8x)+25(y^2-4y)=-36\]
\[4(x-4)^2+25(y-2)^2=-36+4\times 16+25\times 4\]
\[4(x-4)^2+25(y-2)^2=128\]

Answer 3

4*8=32

Answer 4

\[4(x-3)^2+25(y+2)^2\]

right hand side should be
\[-36+4\times 9+25\times 4=100\]

Answer 5

divide by 100 get
\[\frac{(x-3)^2}{25}+\frac{(y+2)^2}{4}=1\]

Answer 6

wow did i mess up sorry. but last step is right

Answer 7

\[4x^2-24x+25y^2+100y=-36\]
\[4(x^2-6x)+25(y^2+4y)=-36\]
\[4(x-3)^2+25(y+2)^2=-36+4\times 9+25\times 4\]
\[4(x-3)^2+25(y+2)^2=100\]