KVPY Sample Paper KVPY Stream-SX Model Paper-3

Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive \[x-\]axis then which of the following points does not lie on it?

A) \[(4-4)\]

B) \[(5,2\sqrt{6})\]

C) (8, 6)

D) \[(6,4\sqrt{2})\]

Correct Answer: C

Solution :

For the parabola vertex\[A=(2,0)\] and focus\[S=(4,0)\]

\[\Rightarrow \] Equation of the parabola is \[{{(y\,-\,0)}^{2}}\,=\,4\,(2)\,(x-2)\]

i.e., \[{{y}^{2}}\,=\,8\,(x-2)\] ?. (1)

The point (8, 6) is not satisfying equation (1).