A parabola touches x-axis and the line y = x respectively at points (1, 0) and (1, 1), then which is /are correct ?

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focus of the parabola is at the point $(\frac{3}{5}, \frac{1}{5})$

slope of axis of the parabola is $\frac{1}{3}$

slope of directrix of the parabola is - 2

focus of the parabola is at the point $(\frac{2}{5}, \frac{4}{5})$

answer is A, D.

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Detailed Solution

$Image of (α, β) in the two tangents are$

$\begin{array}{l} (α, - β) and (β, α) . Slope of axis = \frac{1}{2} \\ {So}_{,} \frac{- β}{α - 1} = \frac{α - 1}{β - 1} = \frac{1}{2} \Rightarrow (α, β) = (\frac{3}{5}, \frac{1}{5}) \end{array}$

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