Parabola 1 Question 3

3. 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?

(2019 Main, 9 Jan, I)

(a) $(4,-4)$

(b) $(6,4 \sqrt{2})$

(c) $(8,6)$

(d) $(5,2 \sqrt{6})$

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Answer:

Correct Answer: 3. (d)

Solution:

  1. 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 $Y^{2}=4 a X$,

where, $X=x-2$ and $Y=y$ and $a=4-2=2$

$\therefore \quad y^{2}=8(x-2)$

Note that $(8,6)$ is the only point which does not satisfy the equation.



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