Axis of a parabola lies along $x -$ 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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Solution

According to the given information, we have the following figure.

Now, if the origin is shifted to $(2, 0)$ and $(X, Y)$ is the point with respect to the new origin, then equation of the parabola is
$Y^{2} = 4 a X$
where,
$X = x - 2$ and $Y = y$ and distance between focus and vertex is $a = 4 - 2 = 2$

$∴$ equation of the parabola is $y^{2} = 8 (x - 2)$
Now, putting the options in this equation we find that $(8, 6)$ is the only point which does not satisfy the equation.

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Similar questions

There is a parabola having axis as $x$ -axis, vertex is at a distance of $2$ unit from origin & focus is at $(4, 0)$ .

Which of the following point does not lie on the parabola.

x

a

a_{1}

x

a

a_{1}

y = x

\sqrt{2}

2 \sqrt{2}

y = x

\sqrt{2}

2 \sqrt{2}

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