1. ## Transformations

Question i've been having difficulty with:

By choosing suitable transformations, express the equation

7x^2 + 90x + 172 + 12xy - 20y - 2y^2 = 0

in the form

AX^2 + BY^2 = 1

any help? x

2. Originally Posted by Shaun Gill
Question i've been having difficulty with:

By choosing suitable transformations, express the equation
7x^2 + 90x + 172 + 12xy - 20y - 2y^2 = 0
in the form
AX^2 + BY^2 = 1
Hello,

- by the different sign of the squares you can see that the graph of this relation must be a hyperbola.
- by the existence of a summand containing xy you can see that the axes of the hyperbola are not parallel to the x- and y-axis. (see attachment)

Unfortunately I haven' found a way to calculate the coordinates of the centre of the hyperbola (that's the point A in the attachment) and to calculate the equation of the axes (the equations of the axes are given with rounded coefficients: line a and b in the attachment)

If you could find the centre then you have to translate the centre to the origin and afterwards rotate the hyperbola counterclockwise.