Question

For the parabola y² = 4x, find the coordinate of the point whose focal distance is 17

Answer 1

Given parabola is y² = 4x

Comparing with y² = 4ax, we get,

4a = 4

∴ a = 1

Let P(x₁, y₁) be he required point on the parabola y² = 4x, whose focal distance is 17.

∴ x₁ + a = 17, where a = 1

∴ x₁ + 1 = 17

x₁ = 16

Since P(x₁, y₁) lies on y² = 4x,

`y_1^2` = 4x₁ 

∴ `y_1^2` = 4(16) = 64

∴ y₁ = ± 8

Hence, coordinates of required points on the parabola are (16, 8) and (16, – 8).