Hi, I'm trying to find variables b and d for this equation of an ellipse using implicit differentiation.

a(x-b)²+c(x-b)(y-d)+k(y-d)²=g

where:

a= 1.2

c= -0.9

k= 2.5

g= 430

I have differentiated it out to make:

dy/dx = 9x+9b+50y50d24x+24b+9y9d

I am not sure how to get b and d from here as the x and y aren't variables I'll have to solve for to create the final function: they will stay in the equation. Not sure how to use simultaneous equations to do something like this, and not sure how to approach it any other way. Am I trying to get these variables too early and have other steps to do first? Could anyone find those two variables for me?

Thank you!