Question

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

2y² = 7x whose parameter is –2

Answer 1

Given equation of the parabola is 2y² = 7x

∴ y² = `7/2x`

Comparing this equation with y² = 4ax, we get

4a = `7/2`

∴ a = `7/8`

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 = `7/8` and t = – 2 in (i), we get

x = `7/8(-2)^2` and  y = `2(7/8)(-2)`

∴ x = `7/2` and y = `-7/2`

∴ The co-ordinates of the point on the parabola are `(7/2, -7/2)`.

Focal distance = x + a = `7/2 + 7/8 = 35/8`