If straight line x cos(alpha) + y sin(alpha) = p touches the curve x2/a2 + y2/b2 = 1 , then prove that a2 cos2(alpha) + b2 sin2(alpha) = p2 .
the given equation of the straight line is :
line (1) is tangent to the curve
for tangent, it must have equal roots, i.e.
which is the required result.
hope this helps you.