Since (a,b) touches the given ellipse 4x2+y2=8 ∴4a2+b2=8 Equation of tangent on the ellipse at the point A(1,2) is: 4x+2y=8⇒2x+y=4⇒y=−2x+4 But, also equation of tangent at P(a,b) is: 4ax+by=8⇒y=
−4a
b
+
8
b
Since, tangents are perpendicular to each other. ⇒