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) (6,42)

(c) (8,6)

(d) (5,26)

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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 Y2=4aX,

where, X=x2 and Y=y and a=42=2

y2=8(x2)

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



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