Help!!

5x^2 + 3y^2 - 20x + 24y = -53       complete the square on x and y

5(x^2 - 4x  + 4)  +  3(y^2 + 8y + 16)  =   -53 + 20 + 48

5(x - 2)^2    +  3 (y + 4)^2  =   15     divide both sides by 15

(x - 2)^2 / 3   +  (y + 4)^2 / 5     =  1

This is an ellipse centered at ( 2 , -4)    with a major axis length  of 2sqrt(5)  and a minor axis length of 2sqrt(3)

Here's the graph : https://www.desmos.com/calculator/kklcz1gncn

5x (to the second power) + 3y (to the second power) - 20x + 24y = -53

I think!:

5x^2 +3y^2 - 20x + 24y +53 =0

\((x-a)^2 + (y-b)^2 = r^2 \text{(equation of circle )} \\ 5x^2+3y^2-20x+24y=-53 \\ 5x^2+3y^2-20x+24y+(2)+(4)=-53+(2)+(4) \\ 5x^2-20x+2+3y^2+24y+4=-47 \\ \text{see } (a+b)^2=a^2+2ab+b^2 \text{and } (a-b)^2=a^2-2ab+b^2 \\ (\sqrt{5}*x-\sqrt{2})^2+(\sqrt{3}*x+2)^2=-53 \)

your equation is WRONG may be you forget smth but i did it anyway just to show you, do the same on your equation