Chapter P.2, Problem 62E

Solution

Choose the correct option for the center of the given circle.

  $\left(3,-4\right)$ , option 1 is correct.

Given information:

The equation of circle ${\left(x-3\right)}^2+{\left(y+4\right)}^2=2$ .

Formula used:

The standard form of equation for circle with center $\left(h,k\right)$ and radius of circle is r is given by

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

Calculation:

In order to find the center and radius of the given circle use the standard form of equation for the circle:

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

Here, $\left(h,k\right)$ represents the center of the circle and r is the radius of circle.

Note that the given equation of circle can be rewritten as:

  $\begin{array}{c}{\left(x-3\right)}^2+{\left(y+4\right)}^2=2\\ {\left(x-3\right)}^2+{\left(y-\left(-4\right)\right)}^2={\left(\sqrt{2}\right)}^2\end{array}$

Comparing it with standard form of equation of circle:

  $\begin{array}{l}h=3,\\ k=-4,\\ r=\sqrt{2}\end{array}$

Thus, the center of circle is $\left(3,-4\right)$ .

Option 1 is correct.