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(i) Tangents are drawn from the point (a...

(i) Tangents are drawn from the point `(alpha, beta)` to the parabola `y^2 = 4ax`. Show that the length of their chord of contact is : `1/|a| sqrt((beta^2 - 4aalpha) (beta^2 + 4a^2))`. Also show that the area of the triangle formed by the tangents from `(alpha, beta)` to parabola `y^2 = 4ax` and the chord of contact is `(beta^2 - 4aalpha)^(3/2)/(2a)`. (ii) Prove that the area of the triangle formed by the tangents at points `t_1 and t_2` on the parabola `y^2 = 4ax` with the chord joining these two points is `a^2/2 |t_1 - t_2|^3`.

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