Math extra credit

[Jessica]

Note: 3^2 means 3 squared. ^ with a number following it means that the number is an exponent.


Directions:

To receive full credot you must do the following:

1. Show OR describe each step of your work, even if you did it in your head ("mental math") or used a calculator.

AND

2. Write an explanation stating the mathematical reason(s) why you chose each of your steps.

A circle is described by the equation (x - 3)^2 + (y - 2)^2 = 25. Determine whether the line y = 4x - 13 is a tangent, secant, secant that contains a diameter, or none of these.

****Check to see if my explanations are okay because I really want to get all 3 bonus points!!!!**** Also, check if my answer is correct!!
DUE TOMORROW!!

1.) Graph circle. (I have that already done)
a. The center of the circle is (3, 2) because the standard equation is (x - h)^2 + (x - k)^2 = r^2. 3 is the h and 2 is the k. The radius of the circle is 5, because I took the square root of 25.
b. Plot the center then count 5 units to the left, right, up, down. make the circle.
2.) Graph line.
a. To graph the line: y = mx + b is the equation. the y-intercept is b and m is the slope. The line given is y = 4x - 13. -13 is the y-intercept and the slope is 4.
3.) To figure out what the line is, you have to know if it goes through the center, it "slices" through the circle, or if it "touches" it.
4.) I graphed it and I found that the line slices through it. It is a secant. However, since it is not going through the center, it would not be a secant containing a diameter.

[Jessica]

please! at least answer this so I know if I did something wrong!

[laepelba]

Jessica - I don't have time to draw the whole thing out to check it. But if you say that it doesn't go through the center, then you are correct that it's not a diameter.

[sosia]

Hi Jessica.
I think you're doing it wrong.
You can use the graphic to confirm your calculations, but you must resolve it from an estric mathematical point of view.
For example.
As you say, the center is 3,2. The line's equation is y = 4x - 13.
Changing the x then 2= 4*3-13, so the line does not pass the center so it's not a secant that contains a diameter.

Using the line and the circle equation, you must find the possible values of x and y, and then see if it's:
a tangent: x has an unique value, both equations have only a common point
a secant: x has two possible values, both equations have only a common point
secant that contains a diameter: no, already explained
or none of these: both equations do not have a common point

Saludos

[Jessica]

Originally Posted by sosia

Hi Jessica.
I think you're doing it wrong.
You can use the graphic to confirm your calculations, but you must resolve it from an estric mathematical point of view.
For example.
As you say, the center is 3,2. The line's equation is y = 4x - 13.
Changing the x then 2= 4*3-13, so the line does not pass the center so it's not a secant that contains a diameter.

Using the line and the circle equation, you must find the possible values of x and y, and then see if it's:
a tangent: x has an unique value, both equations have only a common point
a secant: x has two possible values, both equations have only a common point
secant that contains a diameter: no, already explained
or none of these: both equations do not have a common point

Saludos

I don't understand

[sosia]

Then you do not have all 3 bonus points.
It's math.
Here it's explained, I can not give you more info.
http://home.scarlet.be/~ping1339/circle.htm

Saludos

[Jessica]

oh, well I got all 3 bonus points :P

[Fazor]

Originally Posted by jchen

oh, well I got all 3 bonus points :P

Heh, good job. That's too complicated for me to remember how to do without first grabbing a textbook.

[Jessica]

I knew what to do because we learned about circles and their standard equation and stuff

and thanks!

[Fazor]

Originally Posted by jchen

I knew what to do because we learned about circles and their standard equation and stuff
and thanks!

:-D We learned it too. But that was . . . 12 years ago. And I never did my homework back then anyway :-P