Question

A circle in the xy-plane has a center at G 3 1 42 3 and a radius that is units long. Which of the 15 following is an equation of the circle?

Answer 1

We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle

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

Where (h,k) represents the center of the circunference, and r its radius.

In our example, we obtain that,

`\text{Center}=((3)/(4),(1)/(2))`

And so,

`\begin{gathered} h=(3)/(4),k=(1)/(2) \\ r=(3)/(5) \end{gathered}`

Applying the above formula, we get that the equation of the circle will be:

`(x-(3)/(4))^2+(y-(1)/(2))^2=((3)/(5))^2`

This is:

`\mleft(x-(3)/(4)\mright)^2+\mleft(y-(1)/(2)\mright)^2=(9)/(25)`