This problem has quite a nice solution. The ellipse has equation , and the slope of the tangent at the point (x,y) is given by You want the point to lie on the ellipse, and for the slope there to be
I prefer doing algebra to arithmetic, so I'll write and then substitute in the numerical value when we get to the end of the calculation.
The condition for the point to lie on the ellipse is
The condition for the slope there to be –t is
Solve the second of those equations for a, , and substitute that into the first equation:
After a bit of simplfying and cancellation, that boils down to .
Now you can plug in the value of t, to get . Then substitute that into the equation for to find that