The equation of the diameter of the parabola | vedclass

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(B) The equation of the diameter of a parabola $y^2 = 4ax$ corresponding to a chord with slope $m$ is given by $y = \frac{2a}{m}$.Given the parabola $

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$2y = 1$

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(B) The equation of the diameter of a parabola $y^2 = 4ax$ corresponding to a chord with slope $m$ is given by $y = \frac{2a}{m}$.Given the parabola $y^2 = x$,we have $4a = 1$,so $a = \frac{1}{4}$.The given chord is $x - y + 1 = 0$,which can be written as $y = x + 1$. Thus,the slope $m = 1$.Substituting these values into the formula:$y = \frac{2 	imes (1/4)}{1}$$y = \frac{1/2}{1}$$y = \frac{1}{2}$$2y = 1$.

The equation of the diameter of the parabola $y^2 = x$ corresponding to the chord $x - y + 1 = 0$ is

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