Find the equation of an ellipse if its center is S(2, 1) and the edges of a triangle PQR are tangent lines to this ellipse. P(0, 0), Q(5, 0), R(0, 4).
My attempt: Let take a point on the line PQ. For example (m,0). Then we have an equation of a tangent line for this point: , where etc are coefficients of our ellipse: . Now if PQ: y = 0, then , , .I've tried this method for other 2 lines PR and RQ and I got 11 equations (including equations of a center)! Is there a better solution to this problem?