Given:-
;
, where a is any positive real number.
Consider the helix parabolic equation :

now, take the derivatives we get;

As, we know that two vectors are orthogonal if their dot product is zero.
Here,
are orthogonal i.e, 
Therefore, we have ,




take t common in above equation we get,

⇒
or 
To find the solution for t;
take 
The number
determined from the coefficients of the equation 
The determinant 

Since, for any positive value of a determinant is negative.
Therefore, there is no solution.
The only solution, we have t=0.
Hence, we have only one points on the parabola
i.e <1,0>