Chapter 4.2, Problem 5QR

To determine

To Find: To determine two functions whose graph will combine to get the given curve.

Answer to Problem 5QR

  $y_1=\sqrt{4-{(x-1)}^2}\text{and}{y}_2=-\sqrt{4-{(x-1)}^2}$ .

Explanation of Solution

Given information: Given curve $x^2+y^2=2x+3$ .

Graph:

  

Calculation: From the graph it is clear that the given curve is the equation of a circle with radius 2 and centre (1,0).

Also,

  $\begin{array}{l}{x}^2+y^2=2x+3\\ x^2-2x-3+y^2=0\\ $ {(x-1)}^2-4+y^2=0$$ y^2=4-{(x-1)}^2$y=\pm \sqrt{4-{(x-1)}^2}\\ \text{so,}\\ y_1=\sqrt{4-{(x-1)}^2}\text{and}{y}_2=-\sqrt{4-{(x-1)}^2}\end{array}$

  $y_1=\sqrt{4-{(x-1)}^2}$ represent the curve above the x-axis whereas $y_2=-\sqrt{4-{(x-1)}^2}$ represent the curve below x-axis, combining each of them we get the given circle.