The coordinates of a point on the parabola y^ | vedclass

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Question

(A) The equation of the parabola is $y^2 = 8x$. Comparing this with $y^2 = 4ax$,we get $4a = 8$,so $a = 2$.The focal distance of a point $P(x_1, y_1)$

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$(2, 4)$ and $(2, -4)$

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(A) The equation of the parabola is $y^2 = 8x$. Comparing this with $y^2 = 4ax$,we get $4a = 8$,so $a = 2$.The focal distance of a point $P(x_1, y_1)$ on the parabola $y^2 = 4ax$ is given by $x_1 + a$.Given that the focal distance is $4$,we have $x_1 + 2 = 4$,which implies $x_1 = 2$.Substituting $x_1 = 2$ into the parabola equation $y^2 = 8x$,we get $y^2 = 8(2) = 16$.Therefore,$y = \pm 4$.Thus,the coordinates of the point are $(2, 4)$ and $(2, -4)$.

The coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is $4$ are:

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