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

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

anonymous · Answer

because i did the problem but i think i messed up

anonymous · Answer

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

anonymous · Answer

4*8=32

anonymous · Answer

$$4(x-3)^2+25(y+2)^2$$

right hand side should be 
$$-36+4\times 9+25\times 4=100$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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