If one end of a focal chord of the parabola y | vedclass

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(C) The given parabola is $y^2=8x$. Comparing this with the standard form $y^2=4ax$,we get $4a=8$,so $a=2$. $A$ point on the parabola is given by $(at

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$\frac{25}{2}$

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(C) The given parabola is $y^2=8x$. Comparing this with the standard form $y^2=4ax$,we get $4a=8$,so $a=2$. $A$ point on the parabola is given by $(at^2, 2at) = (2t^2, 4t)$. Given one end of the focal chord is $\left(\frac{1}{2}, 2ight)$,we have $4t=2$,which implies $t=\frac{1}{2}$. The length of a focal chord with parameter $t$ is given by the formula $L = a\left(t + \frac{1}{t}ight)^2$. Substituting $a=2$ and $t=\frac{1}{2}$: $L = 2\left(\frac{1}{2} + \frac{1}{1/2}ight)^2 = 2\left(\frac{1}{2} + 2ight)^2$. $L = 2\left(\frac{5}{2}ight)^2 = 2 	imes \frac{25}{4} = \frac{25}{2}$ units.

If one end of a focal chord of the parabola $y^2=8x$ is $\left(\frac{1}{2}, 2\right)$,then the length of the focal chord is $........$ units.

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