Question

Find the coordinates of points on the parabola y² = 8x whose focal distance is 4.   

Answer 1

We have y² = 8x
⇒ y² = 4(2)x
Comparing it with the general equation of parabola y² = 4ax, we will get a = 2
Let the required point be (x₁, y₁)
Now, Focal distance = 4
⇒ x₁ + a = 4
⇒ x₁ + 2 = 4
⇒ x₁ = 2
Now, the point will satisfy the equation of parabola
∴ (y₁)² = 8(2) = 16
⇒ y₁ = ± 4
Hence, the coordiantes of the points are (2, 4) and (2, −4).