Answer:
b. ellipse; [tex]4x^2+5y^2-40x+60y+260=0[/tex]
Step-by-step explanation:
The graph of [tex]4x^2+5y^2=20[/tex] an ellipse because the coefficients of the quadratic terms are not the same.
This ellipse is centered at the origin. If this ellipse is translated so that its center is now at [tex](5,-6)[/tex].
Then the translated ellipse will now have equation.
[tex]4(x-5)^2+5(y+6)^2=20[/tex]
We expand to get;
[tex]4(x^2-10x+25)+5(y^2+12y+36)=20[/tex]
[tex]4x^2-40x+100+5y^2+60y+180=20[/tex]
[tex]4x^2+5y^2-40x+60y+100+180-20=0[/tex]
[tex]4x^2+5y^2-40x+60y+260=0[/tex]
