Equation of a tangent to the ellipse  x236+y225=1passing through the point where a directrix of the ellipse meets the positive   x-axis is

Equation of a tangent to the ellipse is y=mx+36m2+25                                          (1)Equation of the directrix is x=6×636−25=3611 which meets the   +ve x axis at  3611,0The tangent ( 1) passes through this point if m36112=36m2+25⇒m2=1136⇒m=116.Since the tangent meets the directrix on positive a-axis   m<0  and the required equation is y=−116x+36×1136+256y+11x=36