Question

Where does the point (6,2) lie on a circle centered at (7,8) with a radius of 6

Answer 1

The point lies barely outside of the circle

Explanation:

Equation of a Circle

Given its center (h,k) and radius r, the equation of a circle is given by

`(x-h)^2+(y-k)^2=r^2`

The circle given in the question is centered at (7,8) and has a radius of 6, thus its equation is

`(x-7)^2+(y-8)^2=6^2`

`(x-7)^2+(y-8)^2=36`

To find out if a point (a,b) is outside or inside the circle area, the following conditions apply.

if
`(a-7)^2+(b-8)^2>36` then the point lies outside of the circle area

if
`(a-7)^2+(b-8)^2<36` then the point lies inside of the circle area

Let's use the point as given (6,2)

`(6-7)^2+(2-8)^2=1+36=37`

Thus the point lies barely outside of the circle