If straight line **x cos(alpha) + y sin(alpha) = p** touches the curve **x ^{2}/a^{2} + y^{2}/b^{2} = 1** , then prove that

**a**.

^{2}cos^{2}(alpha) + b^{2}sin^{2}(alpha) = p^{2}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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