Question

Write an equation of a circle giving its Center and radius or diameter.

Answer 1

The equation of a circle with center (h,k) and radius r is given as:

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

From the question, it is given that the center of the circle is (-7,-4) and the diameter is 8.

Since the radius is half the diameter, it follows that the radius is:

`\frac{\text{diameter}}{2}=(8)/(2)=4`

So it implies that r=4, h=-7, and k=-4.

Substitute these values into the equation of a circle:

`\begin{gathered} (x-(-7))^2+(y-(-4))^2=4^2 \\ \Rightarrow(x+7)^2+(y+4)^2=16 \end{gathered}`

Hence, the equation of the circle is:

`(x+7)^2+(y+4)^2=16`