Question

50 points
why do we take any point on a parabola as (at^2 ,2at) ?here t is a parameter.

Answer 1

Answer: we take any point on a parabola as (at^2 ,2at) easiest form to represent the co-ordinates of any point on the parabola y2 = 4ax is (at2, 2at). Since, for all the values of ‘t’ the coordinates (at2, 2at) satisfy the equation of the parabola y2 =  4ax.

Answer 2

1. Write the parametric equations of the parabola y\(^{2}\) = 12x.

Solution:

The given equation y\(^{2}\) = 12x is of the form of y\(^{2}\) = 4ax. On comparing the equation y\(^{2}\) = 12x with the equation y\(^{2}\) = 4ax we get, 4a = 12 ⇒ a = 3.

Therefore, the parametric equations of the given parabola are x = 3t\(^{2}\) and y = 6t.

it is a one common example

help of this examlpe you find the parabola