If the equation of a system of parallel chord | vedclass

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(A) For the parabola $y^2 = 4ax$,we have $4a = 2/3$,which implies $a = 1/6$. Given the system of parallel chords $y + 2x + 1 = 0$,the slope $m$ of the

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$y = -1/6$

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(A) For the parabola $y^2 = 4ax$,we have $4a = 2/3$,which implies $a = 1/6$. Given the system of parallel chords $y + 2x + 1 = 0$,the slope $m$ of these chords is $-2$. The equation of the diameter corresponding to a system of parallel chords with slope $m$ for the parabola $y^2 = 4ax$ is given by $y = \frac{2a}{m}$. Substituting the values $a = 1/6$ and $m = -2$: $y = \frac{2(1/6)}{-2} = \frac{1/3}{-2} = -1/6$. Thus,the equation of the diameter is $y = -1/6$.

If the equation of a system of parallel chords of the parabola $y^2 = \frac{2}{3}x$ is $y + 2x + 1 = 0$,find its diameter.

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