Find the cartesian co-ordinates of the points on the parabola y2 = 12x

1.	Find the cartesian co-ordinates of the points on the parabola y2 = 12x whose parameters are (i) 2(ii) -3
Answer» 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) (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) (ii) Given, t = -3 Substituting a = 3 and t = -3 in (i), we get x = 3(-3)² and y = 2(3)(-3) x = 27 and y = 18 ∴ The cartesian co-ordinates of the point on the parabola are (27, 18)

Find the cartesian co-ordinates of the points on the parabola y2 = 12x whose parameters are (i) 2(ii) -3

Answer»

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)

(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)

(ii) Given, t = -3

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

x = 3(-3)² and y = 2(3)(-3)

x = 27 and y = 18

∴ The cartesian co-ordinates of the point on the parabola are (27, 18)