Chapter 11.1, Problem 49SPR

To determine

To find: The equation of the circle.

Answer to Problem 49SPR

The required equation of the circle is ${\left(x-1\right)}^2+{\left(y+4\right)}^2=17$ .

Explanation of Solution

Given:

The centre of the circle is at $\left(1,-4\right)$ and the diameter of the circle is $r=\sqrt{17}$ .

Calculation:

Consider the formula for the equation of the circle is of the form as,

  ${\left(x-h\right)}^2+\left(y-k^2\right)=r^2$

Here, $\left(h,k\right)$ is the centre and $r$ is the radius.

The centre of the circle is at,

  $\left(h,k\right)=\left(1,-4\right)$

From, the general equation of the circle, the equation of the circle is,

  $\begin{array}{l}{\left(x-h\right)}^2+\left(y-k^2\right)=r^2\\ {\left(x-1\right)}^2+\left(y-{\left(-4\right)}^2\right)={\left(\sqrt{17}\right)}^2\\ {\left(x-1\right)}^2+{\left(y+4\right)}^2=17\end{array}$