Q. 60 - Calculus

Question

For each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation.

${\left(x-1\right)}^2+{\left(y+2\right)}^2=4$

Step-by-Step Solution

Answer

The equation for $y$ is $y=-2\pm \sqrt{4-{\left(x-1\right)}^2}$

Step 1. Given Information

The given equation is ${\left(x-1\right)}^2+{\left(y+2\right)}^2=4$

Step 2. Solve for y

$$\begin{gathered} {\left(x-1\right)}^2+{\left(y+2\right)}^2=4 \\ {\left(y+2\right)}^2=4-{\left(x-1\right)}^2 \\ y+2=\pm \sqrt{4-{\left(x-1\right)}^2} \\ y=-2\pm \sqrt{4-{\left(x-1\right)}^2} \end{gathered}$$

Step 3. Graph of the Equation

We obtained $y=-2\pm \sqrt{4-{\left(x-1\right)}^2}$

The graph is of circle shown in the figure