Question

Find the focal distance of a point on the parabola y² = 16x whose ordinate is 2 times the abscissa

Answer 1

Given equation of the parabola is y² = 16x

Comparing this equation with y² = 4ax, we get

4a = 16

∴ a = `16/4` = 4

 Since ordinate is 2 times the abscissa,

y = 2x

Substituting y = 2x in y² = 16x, we get

(2x)² = 16x

∴ 4x² = 16x

∴ 4x² – 16x = 0

∴ 4x(x – 4) = 0

∴ x = 0 or x = 4,

When x = 4,

focal distance = x + a = 4 + 4 = 8

When x = 0,

focal distance = a = 4

∴ Focal distance is 4 or 8.