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,

$\text{Center}=(\frac{3}{4},\frac{1}{2})$

And so,

$\begin{gathered} h=\frac{3}{4},k=\frac{1}{2} \\ r=\frac{3}{5} \end{gathered}$

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

$(x-\frac{3}{4})^2+(y-\frac{1}{2})^2=(\frac{3}{5})^2$

This is:

$\mleft(x-\frac{3}{4}\mright)^2+\mleft(y-\frac{1}{2}\mright)^2=\frac{9}{25}$