Question

given points (8,6) and ( 8, 0) as the endpoints of a radius ,what is the equation of the circle with center ( 8,6)

Answer 1

Circle Equations

The general equation of a circle is written like
`(x-h)^2+(y-k)^2=r^2`, where (h,k) is the centre and r is the radius.

Solving the Question

Firstly, we're given that the centre is (8,6).

Plug this into the general equation:

`(x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2`

We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.

Therefore, the radius is 6 units. Plug this into the general equation too:

`(x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36`

Answer

`(x-8)^2+(y-6)^2=36`