Question
Given the equation of an ellipse is 4x^2 + y^2 + 24x - 6y + 9 = 0
(i) Find the centre,foci and vertices
(ii)calculate the lengths of the major and minor axes
(i) Find the centre,foci and vertices
(ii)calculate the lengths of the major and minor axes
Answers
Reiny
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 ...
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 ...