Question

The equation (x+6)^2 + (y+4)^2 = 36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.

Answer 1

do you know what shape is represented by that equation?

Answer 2

I'm assuming a circle, because it's like a circle quiz

Answer 3

right. can you find the radius and center of this circle?

Answer 4

I am really bad at geometry and I'm sure I sound dumb saying this, but.. I don't know how, really.

Answer 5

Circle formula:\[(x-h)^2+(y-k)^2=r^2\]

The center of a circle is (h, k). All you have to do to find the center of your circle is pick out the numbers in the h and k spots of your formula and write them in parentheses.

What do you think you center is?

Answer 6

(6,4) ?

Answer 7

close. The signs in the formula are minus. The signs in your equation are positive. So it's really like (x - (-6))² + (y - (-4))².

Basically you just need to remember to switch the sign of whatever's in parentheses. So your center is (-6, -4).

So the source is at (-6, -4).

Answer 8

For the range, you need to find the radius, so take the square root of the number on the right side.

√36 = 6

Answer 9

Ohhh.. So what if it was originally negative? Would i make it positive?

Answer 10

right

Answer 11

I get it. So the circle equation would be the same, just changed to negative?

Answer 12

yes, to find the center

Answer 13

I'm still a little confused? How do I solve to find the center if x and y aren't like terms?

Answer 14

It's not really an equation you solve. You'd need more information to solve for either x or y. All you can do with this equation is find the properties of the circle, like radius, center, diameter, etc.

Answer 15

I still don't get how to find the position and range of the source of a radio signal or describe the position of the source and the range of the signals.

Answer 16

Is thay what finding the radius and center is??

Answer 17

Yes. Your source would be the center of the circle. The range of the signal is the radius.

Let's say you have a graph that represents a map.


There's some type of beacon (source) sending a signal. The source is 6 units left and 4 units down from the origin. This is the center of the circle.


The signal can be hear up to 6 units away. This is the range of the signal AKA radius of the circle.