Find the coordinates of the point on the para | vedclass

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(A) The given equation of the parabola is $y^2 = 8x$. Comparing this with the standard form $y^2 = 4ax$,we get $4a = 8$,which implies $a = 2$. The foc

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$(2, 4)$

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(A) The given equation of the parabola is $y^2 = 8x$. Comparing this with the standard form $y^2 = 4ax$,we get $4a = 8$,which implies $a = 2$. The focal distance of a point $(x, y)$ on the parabola $y^2 = 4ax$ is given by $x + a$. Given that the focal distance is $4$,we have $x + a = 4$. Substituting $a = 2$,we get $x + 2 = 4$,so $x = 2$. Now,substitute $x = 2$ into the parabola equation $y^2 = 8x$: $y^2 = 8(2) = 16$. Therefore,$y = \pm 4$. The points are $(2, 4)$ and $(2, -4)$. Looking at the options,$(2, 4)$ is provided as option $A$.

Find the coordinates of the point on the parabola $y^2 = 8x$ whose focal distance is $4$.

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