Question

Answer the following:

Find the Cartesian coordinates of the point on the parabola y² = 12x whose parameter is 2

Answer 1

Given equation of the parabola is y² = 12x.

Comparing this equation with y² = 4ax, we get

4a = 12

∴ a = 3

If t is the parameter of the point P on the parabola, then

P(t) = (at², 2at)

i.e., x = at² and y = 2at  …(i)

Given, t = 2

Substituting a = 3 and t = 2 in (i), we get

x = 3(2)² and y = 2(3)(2)

∴ x = 12 and y = 12

∴ The cartesian co-ordinates of the point on the parabola are (12, 12).