Stuck on my homework question...again lol...

The tangents of the ellipse with equation x^2/(a^2)+y^2/(b^2)=1 at the points P(acost, bsint) and Q(-asint, bcost) intersect at the point R. (I tried to find R by calculating the equation of the two tangents and then equating them to obtain the x and y coordinates). As t varies, show that R lies on the curve with equation x^2/(a^2)+y^2/(b^2)=2. I then tried to eliminate t to get an equation with just x's and y's but I couldn't eliminate t, so I must have gone wrong. When I tried to get the x-coordinate of R, everything cancelled to 0.

Could someone help please?