Chapter EP, Problem 10.3.4EP

To determine

To calculate; to form the equation for circle satisfying given conditions

Answer to Problem 10.3.4EP

Solution: $x^2+{\left(y-7\right)}^2=49$

Explanation of Solution

Standard form of equation of a circle with center $\left(h,k\right)$ and radius $=r$ is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , in the given question circle is tangent to x-axis and centered at $\left(0,7\right)$ so the point of tangency is $\left(0,0\right)$ . The distance between $\left(0,0\right)and\left(0,7\right)$ is $7$ , so $r=7$

Given $h=0,k=7$ and from above $r=7$ , so after substituting the above values:

$\begin{array}{l}{\left(x-0\right)}^2+{\left(y-7\right)}^2=7^2\\ x^2+{\left(y-7\right)}^2=49\end{array}$