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:
- 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.
