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There si a parabola having axis as x-axi...

There si 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.

A

`(6,8)`

B

`(5,2sqrt(6))`

C

`(8,4sqrt(3))`

D

`(4,-4)`

Text Solution

Verified by Experts

The correct Answer is:
C
According to given information, we have the following figure.

Now, if the origin is shifted to (2,0) and (X,Y) are the coordinates with respect to new origin, then equation of parabola is `Y^(2) = 4aX`,
where, `X = x - 2` and `Y = y` and `a = 4 - 2 = 2`
`:. y^(2) = 8(x - 2)`
Note that (8,6) is the only point which does not satisfy the equation.
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