Chapter 4.2, Problem 4QR

To determine

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

Answer to Problem 4QR

  $y_1=\sqrt{9-x^2}\text{and}{y}_2=-\sqrt{9-x^2}$

Explanation of Solution

Given information: Given curve $x^2+y^2=9$

Graph:

  

Calculation: From the graph it is clear that the given curve is the equation of a circle with radius 3 and Centre (0,0).

Also,

  $\begin{array}{l}{x}^2+y^2=9\\ y^2=9-x^2\\ y=\pm \sqrt{9-x^2}\\ \text{so,}\\ y_1=\sqrt{9-x^2}\text{and}{y}_2=-\sqrt{9-x^2}\end{array}$

  $y_1=\sqrt{9-x^2}$ represent the curve above the x-axis whereas $y_2=-\sqrt{9-x^2}$ represent the curve below x-axis, combining each of them we get the given circle.