Question

The maximum distance from origin of a point on the curve x = `a sin t - b sin((at)/b)`, y = `a cos t - b cos((at)/b)`, both a, b > 0 is ______.

Options

• a – b

• a + b

• `sqrt(a^2 + b^2)`

• `sqrt(a^2 - b^2)`

Answer 1

The maximum distance from origin of a point on the curve x = `a sin t - b sin((at)/b)`, y = `a cos t - b cos((at)/b)`, both a, b > 0 is a + b.

Explanation:

We know that distance of origin from

(x, y) = `sqrt(x^2 + y^2)`

= `sqrt(a^2 + b^2 - 2ab cos(t - (at)/b)`;

`≤ sqrt(a^2 + b^2 + 2ab)[{cos(t - (at)/b)}_min = -1]`

= a + b

∴ Maximum distance from origin = a + b