Q.38 - Precalculus Enhanced with Graphing Utilities

Question

Find the standard form of the equation of each circle.

Center (-3, 1) and tangent to the y-axis

Step-by-Step Solution

Answer

The standard form of the equation of circle at the center(-3,1) and tangent to the y-axis is ${(x+3)}^2+{(y-1)}^2=9$.

Step 1. Given information

Given that circle at the center (-3,1)  and tangent to y-axis.

 we have to find the standard form of the equation for the circle

Step 2. Description of finding the radius r of a circle

To find the equation of the circle, first, we need to know about the radius. Here circle centered at (-3,1 )  and tangent to the y-axis, tangency point is (0,1). So the distance between this theses two is the radius, then the radius is 3.

Step 3. Finding the standard of the equation of a circle

 Here radius is 3 and the standard form of  the equation of a circle is $$\begin{gathered} {(x-h)}^2+{(y-k)}^2=r^2 , (h, k) is point at the center \\ {(x+3)}^2+{(y-1)}^2=3^2 \\ {(x+3)}^2+{(y-1)}^2=9 . \end{gathered}$$