Answer:
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x =
and y =
where and
are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x =
=
y =
=
Therefore, coordinates of pint B will be,
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>
