Question

Answer the following:

Find the co-ordinates of a point of the parabola y² = 8x having focal distance 10

Answer 1

Given equation of the parabola is y² = 8x 

Comparing this equation with y² = 4ax, we get

4a = 8

∴ a = 2

Focal distance of a point = x + a

Given, focal distance = 10

∴ x + 2 = 10

∴ x = 8 

Substituting x = 8 in y² = 8x, we get

y² = 8(8)

∴ y = ± 8

∴ The co-ordinates of the points on the parabola are (8, 8) and (8, –8).