The student council is planning for the prom. They have broken down their expenses in the graph below. If they decide they will
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First thing to do is to move the constant over to the other side of the equals sign. Then we will complete the square on the x terms. We will take half the linear term, square it, then add it to both sides. Our linear term is 4. Half of 4 is 2, and 2 squared is 4. 
. In the process of completing the square we have created a perfect square binomial on the left which is 
. A is our answer.
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>