If the line ax+ by =1 passes through t...

If the line `ax+ by =1` passes through the point of intersection of `y =x tan alpha + p sec alpha, y sin(30^@-alpha)-x cos (30^@-alpha) =p`, and is inclined at `30^@` with `y=tan alpha x` , then prove that `a^2 + b^2 = 3/(4p^2)` .

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