Question

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

y² = 12x whose parameter is `1/3`

Answer 1

Given parabola is y² = 12x

Comparing with y² = 4ax, we get,

4a = 12

∴ a = 3 

If a point P has parameter t, then P(t) = (at², 2at)

Here, t = `1/3`

∴ P`(1/3) = (3 xx 1/9, 2 xx 3 xx 1/3)`

= `(1/3, 2)`

Focal distance of P

= a + x₁, where x₁ = `1/3`

= `3 + 1/3`

= `10/3`