Find coordinates of the point on the parabola. Also, find focal distan

1.	Find coordinates of the point on the parabola. Also, find focal distance: y2 = 12x whose parameter is 1/3
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) Given, t = 1/3 Substituting a = 3 and t = 1/3 in (i), we get x = 3 (1/3)²and y = 2(3)(1/3) x = 1/3 and y =2 The co-ordinates of the point on the parabola are (1/3, 2) ∴ Focal distance = x + a = 1/3 + 3 = 10/3

Find coordinates of the point on the parabola. Also, find focal distance: y2 = 12x whose parameter is 1/3

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)

Given, t = 1/3

Substituting a = 3 and t = 1/3 in (i), we get

x = 3 (1/3)²and y = 2(3)(1/3)

x = 1/3 and y =2

The co-ordinates of the point on the parabola are (1/3, 2)

∴ Focal distance = x + a

= 1/3 + 3

= 10/3