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The midpoint of chord $2 x + y - 5 = 0$ of the parabola $y^{2} = 4 x$ is

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$(1, 3)$

$(3, - 1)$

$(\frac{5}{2}, 0)$

$(2, 1)$

answer is C.

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Detailed Solution

$A (x_{1}, y_{2}) B (x_{2}, y_{2})$

Mid point = $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

$(h, k) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

$2 x + y - 5 = 0 \Rightarrow y = 5 - 2 x$

$y^{2} = 4 x \Rightarrow {(5 - 2 x)}^{2} = 4 x$

$x_{1} + x_{2} = 6, h = 3 y^{2} = 4 x$

$K = - 1 y^{2} = 2 (4 - y)$

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