2. For the circle with equation (x – 2)2 + (y + 3)2 = 9, what is the diameter and radius of the circle?

Question

2.	For the circle with equation (x – 2)2 + (y + 3)2 = 9, what is the diameter and radius of the circle?

kainui · Answer

So try to tell me everything you know about this equation. Maybe if you graph a few random points it will make it clearer.

anonymous · Answer

I think the coordinates are (2, -3) and and radius is 4.5 with a diameter of 9?

kainui · Answer

Not quite. What are those coordinates supposed to represent? Also, how did you find the radius to be 4.5?

anonymous · Answer

the coordinates are supposed to represent the center of the circle. I'm guessing those of the right coordinates given from the information. and the Radius must be 3 right? Do you just fine the square root of the nine?

anonymous · Answer

?

kainui · Answer

Yeah, the square root of 9 is the radius. But basically all this formula is, is simply the pythagorean theorem. Also, the coordinates for the center are actually negative of what you've written.

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See how the radius is the hypotenuse? That's why the square root of that 9 is the radius.

Why is it that the center is negative of what you think it should be? Well, that's because you have to plug in the negative of that number to cancel it out. For instance, if you plug in x=-2 what do you get for y?

anonymous · Answer

it would become positive 2?

kainui · Answer

What would become positive 2?

kainui · Answer

$$\Large (x – 2)^2 + (y + 3)^2 = 9$$ Sorry I should have told you to plug in x=2 or y=-3. My bad! If you plug in -2 you will have to take the square root of a negative number, so you know there is not point where x=-2 lies on the circle!

So for x=2
$$\Large (2 – 2)^2 + (y + 3)^2 = 9$$$$\Large  (y + 3)^2 = 9$$$$\Large  y + 3 = \pm 3$$
See how I left a plus or minus sign there in front of the 3? That's because we stook the square root and (-3) squared is the same as (3) squared, so either one is possible.

so our answers are:
$$\Large  y =0$$$$\Large y=-6$$

Notice how one is the top of the circle and the other is the bottom of the circle? They're even 6 points apart, which is the diameter, since the radius is 3! So we know that this has to be the middle x-value. And the middle y-value must be -3 as well to be between these two points. Does this make sense?