Write the Standard Form of the Equation for this Circle

[nycmathguy]

Homework Statement

Write standard form of the equation of a circle.

Relevant Equations

Equation of a circle not centered at the origin.

(x - h)^2 + (y - k)^2 = r^2

Chapter 1, Section 1.2

Write the standard form of the equation of the circle with the given characteristics.

74. Endpoints of a diameter: (11, −5), (3, 15)

I want to know if the following steps are correct for me to answer the above question.

Steps:

1. Find the distance between the points.

2. Divide the distance by 2 to find the radius.

3. Plug into (x - h)^2 + (y - k)^2 = r^2

You say?

 

[berkeman]

Homework Statement:: Write standard form of the equation of a circle.
Relevant Equations:: Equation of a circle not centered at the origin.

(x - h)^2 + (y - k)^2 = r^2

Steps:

1. Find the distance between the points.

2. Divide the distance by 2 to find the radius.

3. Plug into (x - h)^2 + (y - k)^2 = r^2

Looks reasonable so far, but how do you use those two endpoints to find h and k?

 

[cbarker1]

Do you know the midpoint formula?

 

[nycmathguy]

Do you know the midpoint formula?

Yes, I know the midpoint formula. What about it?

 

[nycmathguy]

Looks reasonable so far, but how do you use those two endpoints to find h and k?

I would plug the x and y values of the endpoints in the standard form of an equation of a circle to find h and k. Yes?

 

[berkeman]

I would plug the x and y values of the endpoints in the standard form of an equation of a circle to find h and k. Yes?

Sorry, I have no idea what that means. Instead, I would follow this hint:

Do you know the midpoint formula?

 

[phinds]

You say?

I say that once again, you are not following through.

Draw the two points on a graph. Calculate the midpoint numerically and see if it looks right on the graph. When you have the midpoint, write the equation of the circle. There's more for a full follow-through.

 

[SammyS]

Yes, I know the midpoint formula. What about it?

How is the mid-point of a diameter of a circle related to the location of the circle's center ?

 

[cbarker1]

Yes, I know the midpoint formula. What about it?

So what is the formula, then?

 

[nycmathguy]

How is the mid-point of a diameter of a circle related to the location of the circle's center ?

The midpoint of a circle divides the diameter into two radii.

 

[SammyS]

The midpoint of a circle divides the diameter into two radii.

I asked about the mid-point of a diameter of a circle. How is the mid-point related to the center of the circle?

 

[phinds]

The midpoint of a circle divides the diameter into two radii.

Quite futzin' around just DRAW it and get on with solving the problem. I don't understand why you have such an issue with follow through. You are going to keep having trouble with these problems if you don't get past that issue.

 

[nycmathguy]

Quite futzin' around just DRAW it and get on with solving the problem. I don't understand why you have such an issue with follow through. You are going to keep having trouble with these problems if you don't get past that issue.

Follow through in what way? I'm stuck here.

 

[nycmathguy]

I asked about the mid-point of a diameter of a circle. How is the mid-point related to the center of the circle?

Midpoint = [(11 + 3)/2, (-5 +15)/2]

Midpoint = (14/2, 10/2)

Midpoint = (7, 5)

This point = (h, k) = (7, 5).

So, h = 7 and k = 5.

I now plug into (x - h)^2 + (y - k)^2 = r^2.

Wait, I need the radius.

To find the radius, I must use the distance formula points.

So far, so good, yes?

 

[nycmathguy]

Quite futzin' around just DRAW it and get on with solving the problem. I don't understand why you have such an issue with follow through. You are going to keep having trouble with these problems if you don't get past that issue.

I found h to 7 and k to be 5.

My friend completed the problem.

Here is her work:

distance between center (7,5) and point (3, 15) is the length of radius:

r=sqrt((7-3)^2+(5-15)^2)
r=sqrt(4^2+(-10)^2)
r=sqrt(16+100)
r=sqrt(116)

then r^2=116
(x - 7)^2 + (y - 5)^2 = 116=> your equation

 

[phinds]

Follow through in what way? I'm stuck here.

Do you not understand how to put points on a graph?

 

[nycmathguy]

Do you not understand how to put points on a graph?

Forget it. Problem has been solved.