Find the length of the chord intercepted by t | vedclass

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(B) The equation of the parabola is $y^2 = 64x$,so $4a = 64$,which gives $a = 16$.The equation of the line is $4y = 3x - 48$,which can be written as $

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$\frac{1600}{9}$

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(B) The equation of the parabola is $y^2 = 64x$,so $4a = 64$,which gives $a = 16$.The equation of the line is $4y = 3x - 48$,which can be written as $y = \frac{3}{4}x - 12$. Here,$m = \frac{3}{4}$ and $c = -12$.The length of the chord intercepted by the line $y = mx + c$ on the parabola $y^2 = 4ax$ is given by the formula $L = \frac{4}{m^2} \sqrt{a(1+m^2)(a-mc)}$.Substituting the values: $L = \frac{4}{(3/4)^2} \sqrt{16(1 + (3/4)^2)(16 - (3/4)(-12))}$.$L = \frac{4}{9/16} \sqrt{16(1 + 9/16)(16 + 9)}$.$L = \frac{64}{9} \sqrt{16(\frac{25}{16})(25)}$.$L = \frac{64}{9} \sqrt{25 	imes 25} = \frac{64}{9} 	imes 25 = \frac{1600}{9}$.

Find the length of the chord intercepted by the line $4y = 3x - 48$ on the parabola $y^{2} = 64x$.

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