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Area between x=g(y) and y Axis

If the line x...

Question

If the line x-3y+k =0 touches the parabola $3 y^{2} = 4 x$ then the value of k is

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Solution

The correct option is D
3

$\begin{matrix} x - 3 y + k = 0 & 3 y^{2} = 4 x 3 y = x + k & y^{2} = \frac{4}{3} x y = \frac{1}{3} x + \frac{k}{3} & a = \frac{1}{3} \end{matrix} c = \frac{a}{m} \Rightarrow \frac{k}{3} = \frac{\frac{1}{3}}{\frac{1}{3}} = 1 \Rightarrow k = 3$

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