Question

Question #d317a

Answer 1

`(x-a)^2+(y-b)^2=49/4`

Explanation:

Here, remember that the equation of a circle is like the following:
`(x-a)^2+(y-b)^2=r^2` where the center of the circle is `(a,b)` and `r` is the radius of the circle. `x` and `y` are the variables.

Since we are only given the diameter of a circle, we try to find the radius.
Remember that `d=2r`

Therefore, `2r=7`
=>`r=7/2`

We plug this into our standard form of `(x-a)^2+(y-b)^2=r^2`
=>`(x-a)^2+(y-b)^2=(7/2)^2`
=>`(x-a)^2+(y-b)^2=49/4`

That is our answer!

Now, this equation is telling us this: Any point that is `49/4` units away from the center `(a,b)` applies to the equation.