Question

If a circle rolls along a horizontal line without slippage, a fixed point P on the circle will trace out a curve called $a\left(n\right)$.

Short answer

it traces out a cycloid

Step-by-step solution

Step 1. Description

Given that a circle rolls along a horizontal line without slippage.

To find out the name of curve traced out by the fixed point P of the circle on the horizontal line.

Step 2. Simplification

when one curve rolls over another curve without slipping or sliding, the path of any point of the rolling curve is called roulette.

When the rolling curve is a circle and the curve on which it rolls is a straight line, it traces out a cycloid.