The axis of a parabola lies along the x-axis. | vedclass

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(B) The vertex is at $(2, 0)$ and the focus is at $(4, 0)$.Since the axis is the $x$-axis,the parabola opens to the right.The distance between the ver

Vedclass · Accepted Answer

$(8, 6)$

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(B) The vertex is at $(2, 0)$ and the focus is at $(4, 0)$.Since the axis is the $x$-axis,the parabola opens to the right.The distance between the vertex and the focus is $a = 4 - 2 = 2$.The equation of the parabola is $(y - 0)^2 = 4a(x - 2)$,which simplifies to $y^2 = 8(x - 2)$.Now,we check each option:$A$: $y^2 = (2\sqrt{6})^2 = 4 	imes 6 = 24$ and $8(5 - 2) = 8 	imes 3 = 24$. (Lies on parabola)$B$: $y^2 = 6^2 = 36$ and $8(8 - 2) = 8 	imes 6 = 48$. Since $36 
eq 48$,$(8, 6)$ does not lie on the parabola.$C$: $y^2 = (4\sqrt{2})^2 = 16 	imes 2 = 32$ and $8(6 - 2) = 8 	imes 4 = 32$. (Lies on parabola)$D$: $y^2 = (-4)^2 = 16$ and $8(4 - 2) = 8 	imes 2 = 16$. (Lies on parabola)Thus,the point $(8, 6)$ does not lie on the parabola.

The axis of a parabola lies along the $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin on the positive $x$-axis,then which of the following points does not lie on it?

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