# What is the equation of the locus of points at a distance of #sqrt(20)# units from #(0,1)#? What are the coordinates of the points on the line #y=1/2x+1# at a distance of #sqrt(20)# from #(0, 1)#?

##### 1 Answer

Equation:

Coordinates of specified points:

#### Explanation:

**Part 1**

The locus of points at a distance of

is the circumference of a circle with radius

The general form for a circle with radius

In this case

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**Part 2**

The coordinates of the points on the line

are the intersection points of

Substituting

Either

or