Finding equations of tangents parallel to y-axis, not sure how to proceed

Hello Mr Koh,

                        I recently encountered a problem in my holiday revision package which asked us to discover the equations of the tangents to the curve  x^2- axy +y^2 =a  which are parallel to the y-axis. I managed to compute an expression via implicit differentiation for the gradient function, ie dy/dx = (ay-2x)/ (2y-ax) which I am not sure if it is correct; I also do not really know how to proceed from here. Could you please advise?

Student X

Hi,

     The expression for dy/dx obtained is absolutely accurate. With regards to finding the necessary tangent equations, you shall have to set dx/dy=0 , thereafter inject the result arising from this back into the original curve equation. Kindly find my set of workings in full below, hope it helps. Peace.

Best Regards,

Mr Koh