Circle that is tangent?

[shawie]

I know that tangent means... touching right? but i don't get these questions, and how to approach them.. I have to write an equation of the circles:

The center is (5, -4) and the circle is tangent to the axis.

The circle is tangent to the x-axis at (4,0) and has y-intercepts -2 and -8.

 

[soroban]

Hello, shawie!

I assume you know the general equation for a circle . . .

The equation of a circle is: \(\displaystyle \x\,-\,h)^2\,+\,(y\,-\,k)^2\:=\:r^2\)
\(\displaystyle \;\;\)where \(\displaystyle (h,k)\) is the center and \(\displaystyle r\) is the radius.

Did you make a sketch? . . . I doubt it.

The center is (5, -4) and the circle is tangent to the axis.

Tangent to which axis?

Assuming the circle is tangent to the x-axis (the closer one), the graph looks like this:

      |        5
    --+-------***------
      |    *       *
      |  *           *
      | *             *
     4+ *      *      *
      | *             *
      |  *           *
      |    *       *
      |       ***

You already know the center: \(\displaystyle (h,k)\,=\,(5,\,\)-\(\displaystyle 4)\)

Can you figure out \(\displaystyle r\), the length of the radius ?

 

[galactus]

Try not to get put off by these circle problems. Try to picture the circle intercepting the y axis at -2 and -8. Your y-coordinate for the center will be what is halfway in between -2 and -8. What is that?. Since it is tangent to the x-axis at (4,0), what then is the x-coordinate of the center?. Once you have the center, you've got it kicked.

For the first one.....which axis is it tangent to?.

 

[shawie]

ohh ok, yes it is tangent to the x-axis. do you always have to make a sketch? ..there's not formula i can use to figure that out?

is the radius for the 1st one 4?

 

[soroban]

Hello, shawie!

Do you always have to make a sketch?

No, if you have enough brain cells (I don't!), you can simply <u>visualize</u> the problem.

Is there a formula for every possible circle problem they can ask?
\(\displaystyle \;\;\)Sure, we can create a list of formulas for every possible question.
\(\displaystyle \;\;\)It'll be the size of the Manhattan phonebook and the look-up time may be <u>days</u>.
Then, someday, someone will ask a new question . . . and we're screwed.
\(\displaystyle \;\;\)(And that's just circles . . . there are triangles, rectangles, etc.)

is the radius for the 1st one 4?

Yes . . . but can't you see that from my diagram?

 

[shawie]

lol alright, thank you all so much