Given the equation of an ellipse is 4x^2 + y^2 + 24x - 6y + 9 = 0

Question

(i) Find the centre,foci and vertices
(ii)calculate the lengths of the major and minor axes

Answer 1

complete the square ....

4(x^2 + 6x + ...) + *y^2 - 6y + .....) = -9

4(x^2 + 6x + 9) + *y^2 - 6y + 9) = -9 + 36 + 9
4(x+3)^2 + (y+3)^2 = 36
divide by 36

(x+3)^2 /9 + (y+3)^2 /36 = 1

take it from here ...