We have to determine the equations of the tangents drawn from the point P(5,-3) to the ellipse x² + 4y² + 2x +2x-12y + 6 = -(1) Differentiating with respect to x 2x+8ydy + 2- x² + 4y² + 2x-12y+6=0 dy ds dy (8y- 12) = (2x+2) ds or dy ds = = - 12d4 = 0 -(x+1) 4y-6 x+1 2(3-2y) - x+1 2(3-2y) or. 2(y + 3) (3-2y) = (x + 1)(x - 5) or, The equations of tangents drawn from the point are. P (5,-3) to the ellipse (1) y+3= (x-5) we 2 get. x-5xx-5 2(Зу+9-2у2-бу) 2. -18²-6y +18 = x²=4x-5 x² + 4y²-4x+6y-23 -23 = 0