Identify the graph of 4x^2+5y^2=20 for T(5,-6) and write an equation of the translated or rotated graph in general form. (picture provided)

Accepted Solution

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]