Question

Write the equation of the circle given the following information.Center: (-4,3)Diameter: 9

Answer 1

The equation of a circle is given by:

`\lparen x-h)\placeholder{⬚}^2+\left(y-k\right)^2=r^2`

where (h,k) is the center and r is the radius.

In this case we know that the center of the circle is (-4,3). To find the radius we just need to remember that the radius is half the diameter, hence:

`r=(9)/(2)`

Plugging the values for the center and the radius we have that:

`\begin{gathered} \lparen x-\left(-4\right))\placeholder{⬚}^2+\left(y-3\right)^2=\lparen(9)/(2))^2 \\ \lparen x+4)\placeholder{⬚}^2+\left(y-3\right)^2=(81)/(4) \end{gathered}`

Therefore, the equation of the circle is: