Chapter 9.3, Problem 55PPS

To determine

To Find: The equation for the circle that satisfies the condition.

Answer to Problem 55PPS

  ${(x-2.5)}^2+{(y-2.5)}^2=6.25$

Explanation of Solution

Given: Center in the first quadrant, tangent to $x=5$ , the $xaxis$ , $yaxis$

Center in the first quadrant, tangent to $x=5$

Here

  $\begin{array}{l}h>0\\ k>0\\ C(h,k)\\ x=5\end{array}$

Diameter = $5$

Thus

  $\begin{array}{l}h=\frac{5}{2}=2.5\\ k=2.5\end{array}$

Equation of the circle

  $\begin{array}{}$ {(x-h)}^2+{(y-k)}^2=r^2$$ {(x-2.5)}^2+{(y-2.5)}^2={2.5}^2$$ {(x-2.5)}^2+{(y-2.5)}^2=6.25$\end{array}$

Hence, ${(x-2.5)}^2+{(y-2.5)}^2=6.25$