Chapter 8, Problem 14T

Solution

Write the standard form of the equation of the conic section with the given characteristics.

  ${\left(x-9\right)}^2+{\left(y+1\right)}^2=4$

Given information:

Given circle with centre at $\left(9,-1\right)$ and radius $2$ .

Formula used:

Standard form of equation of a circle with radius ‘ r’ and center $\left(h,k\right)$ is

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

Calculation:

In order to write the standard form of the equation of the circle with the given center and radius, use the standard form of the equation of the circle:

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , with radius ‘ r’ and centre $\left(h,k\right)$ .

Note that the centre of given circle is $\left(9,-1\right)$ and the radius of the circle is $2$ , i.e. here

  $\left(h,k\right)=\left(9,-1\right),r=2$

Thus, the equation becomes:

  $\begin{array}{c}{\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2\\ {\left(x-9\right)}^2+{\left(y-\left(-1\right)\right)}^2={\left(2\right)}^2\\ {\left(x-9\right)}^2+{\left(y+1\right)}^2={\left(2\right)}^2\\ {\left(x-9\right)}^2+{\left(y+1\right)}^2=4\end{array}$

Thus, the standard form of the equation of circle with given information is:

  ${\left(x-9\right)}^2+{\left(y+1\right)}^2=4$