Chapter 13, Problem 2CV

Solution

To fill: Centred at the origin of the coordinate plane, the ...... has a radius of $1$ unit.

“Centred at the origin of the coordinate plane, the unit circle has a radius of $1$ unit.”

Given:

The blank to fill is, “Centred at the origin of the coordinate plane, the ...... has a radius of $1$ unit.”

Explanation:

By definition of a circle, “A circle is the locus of a point $P\left(x,y\right)$ whose distance from a fixed point $\left(h,k\right)$ say centre of the circle is always constant. And by distance formula the equation of circle is written as ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ where $\left(r\right)$ represents the radius of the circle. And, if centre $\left(h,k\right)=\left(0,0\right)$ and radius $\left(r\right)=1$ , then then equation becomes $x^2+y^2=1$ which represents a unit circle.

Therefore, the blank is filled as, “Centred at the origin of the coordinate plane, the unit circle has a radius of $1$ unit.”

Conclusion:

The blank is filled as, “Centred at the origin of the coordinate plane, the unit circle has a radius of $1$ unit.”