Question
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.
$$\left( {5,\,2\sqrt 6 } \right)$$
B.
$$\left( {8,\,6} \right)$$
C.
$$\left( {6,\,4\sqrt 2 } \right)$$
D.
$$\left( {4,\, - 4} \right)$$
Answer :
$$\left( {8,\,6} \right)$$
Solution :
Since, vertex and focus of given parabola is $$\left( {2,\,0} \right)$$ and $$\left( {4,\,0} \right)$$ respectively
Then, equation of parabola is
$$\eqalign{ & {\left( {y - 0} \right)^2} = 4 \times 2\left( {x - 2} \right) \cr & \Rightarrow {y^2} = 8x - 16 \cr} $$
Hence, the point $$\left( {8,\,6} \right)$$ does not lie on given parabola.
Since, vertex and focus of given parabola is $$\left( {2,\,0} \right)$$ and $$\left( {4,\,0} \right)$$ respectively
Then, equation of parabola is
$$\eqalign{ & {\left( {y - 0} \right)^2} = 4 \times 2\left( {x - 2} \right) \cr & \Rightarrow {y^2} = 8x - 16 \cr} $$
Hence, the point $$\left( {8,\,6} \right)$$ does not lie on given parabola.