Question

Help with this exercise is it asking me if there is all the equations or just 1

Answer 1

For this problem, we are given a circle on the coordinate plane, and we need to determine its expression.

The first step to finding the expression is to determine the center of the circle, the coordinates for the center are:

`C(5,2)`

Now we need to find the radius, which is the distance from the center to the circumference. We have:

`R=4`

We can represent the circle as:

`(x-A)^2+(x-B)^2=R^2`

Where (A,B) are the coordinates for the center of the circle and R is the radius. Applying the values we calculated from the image, we have:

`\begin{gathered} (x-5)^2+(y-2)^2=4^2 \\ x^2-10x+25+y^2-4y+4=16 \\ x^2-10x+y^2-4y+29=16 \\ x^2-10x+y^2-4y=16-29 \\ x^2-10x+y^2-4y=-13 \end{gathered}`

The correct option is (2).