Question
If two of the three feet of normals drawn from a point to the parabola $${y^2} = 4x$$ be $$\left( {1,\,2} \right)$$ and $$\left( {1,\, - 2} \right)$$ then the third foot is :
A.
$$\left( {2,\,2\sqrt 2 } \right)$$
B.
$$\left( {2,\, - 2\sqrt 2 } \right)$$
C.
$$\left( {0,\,0} \right)$$
D.
none of these
Answer :
$$\left( {0,\,0} \right)$$
Solution :
The sum of the ordinates of the feet $$ = {y_1} + {y_2} + {y_3} = 0$$
$$\eqalign{
& \therefore \,2 + \left( { - 2} \right) + {y_3} = 0 \cr
& \therefore \,{y_3} = 0 \cr} $$