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.

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