Chapter 13.7, Problem 21PSC

To determine

To find: The equation of the circle on which the B lies.

Answer to Problem 21PSC

The equation of the circle is ${\left(4+x\right)}^2+y^2=36$ .

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The line OA is fixed segment and point M lie anywhere on the circle with the radius 3 and the centre is O.

The point B moves such that M is the midpoint of AB line.

Calculation:

Consider the midpoint of AB is obtained as,

  $M=\left(\frac{4+x}{2},\frac{y}{2}\right)$

Consider the point M is on the circle with the equation of the circle as $x^2+y^2=9$ . Then,

  $\begin{array}{l}{\left(\frac{4+x}{2}\right)}^2+y^2=9\\ {\left(4+x\right)}^2+y^2=36\end{array}$