In the following exercises, (a) find the center-radius form of th...

Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6.

center (5, -4), radius 7

Accepted Answer

Hello, everyone. We are asked to find the center radius form of the circle using the given information and plot it on the rectangular coordinate system. We are told the center is the 0.11 negative seven and the radius is five. We are given a coordinate plane where the X and Y axis both are in the scale of one and the X axis has denoted points from negative 20 to 20. And the Y has a range of negative 15 to 15. First. We need to recall what is the setup for the center radius form? Well, that is a parentheses with X minus H squared plus a set of parentheses, Y minus K squared equals R squared. R is going to represent our radius and HK is the coordinates of our center. So now that we have the format down, let's see if we can plug in what we're given. So we are told our center is 11 negative seven and our radius is five. So we're gonna leave X and Y in the form itself. So open parentheses, X minus H so H is the X value of the center which is 11 closed parentheses squared. Plus open parentheses. Why minus K? So K is the Y value of the center which is negative seven. So for subtracting negative seven, the same as adding seven closed parentheses squared equals our radius which is five squared. So this is the equation in center radius form. So now we wanna plot that on our coordinate system. So I'm starting with my center is at the 0.11 negative seven. So right about here and then if I have a radius of five, I'm gonna go out on this line negative 712345. I'm gonna go up from the center 12345. I'm going to go to the left from the center 12345. And I'm gonna go down from the center 12345. That way I have landmarks to help me draw my circle. So our circle lands in the fourth quadrant, it has a radius of five and the center is at the 0.11 negative seven. Have a nice day.

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (5, -4), radius 7

Key Concepts

Center-Radius Form of a Circle

Graphing a Circle

Coordinate Geometry

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