what is the foci of the ellipse(25x^2+9y^2-150x=0

Question

find foci of the ellipse

Answer 1

The equation of the ellipse is Ax^2 +By^2+Dx+Ey+F=0

In our case;

A=25,C= 9,D= -150. we also need the following: center; h=(-D/2A)=150/50 = 3; k= 0/2C=0. center is on point (3,0). a=√C=3 and b=√A =5. Then we see that the major axis is in the Y axis sense. to calculate the foci we have c=foci distance=√(5^2-3^2) =√16 =4. then the coordinates for the foci are (3,4) and (3,-4). It is correct because the distance a is greater than the foci distance.