Circle P has a radius of 8 units with center P at (2, -1). Which equation defines circle P?

(x + 2)^2 + (y – 1)^2 = 64

(x – 2)^2 + (y + 1)^2 = 64

(x – 2)^2 + (y + 1)^2 = 8

(x + 2)^2 + (y – 1)^2 = 8

Question

Circle P has a radius of 8 units with center P at (2, -1). Which equation defines circle P?

 (x + 2)^2 + (y – 1)^2 = 64

 (x – 2)^2 + (y + 1)^2 = 64

 (x – 2)^2 + (y + 1)^2 = 8

 (x + 2)^2 + (y – 1)^2 = 8

zepdrix · Answer

Equation of a circle:
$$\large(x-h)^2+(y-k)^2=r^2$$
So our radius is 8. Looking at the equation, what should r^2 be?

zepdrix · Answer

This equation is for a circle centered at (h,k), sorry I forgot to mention that. :)

anonymous · Answer

sorry, i'm still stuck on whether it's C or D /:

zepdrix · Answer

We can immediately determine that it is neither C nor D.
If our Radius = 8

Then our Radius Squared (in the equation) = 64 yes?

anonymous · Answer

ohh

zepdrix · Answer

$$(x-h)^2+(y-k)^2=r^2$$
Plugging in our center points and our radius, gives us this:
$$(x-2)^2+(y-(-1))^2=8^2$$

The negative signs inside the brackets might be a little confusing. The equation is defined with -h and -k, so we should get the opposite of our coordinates inside the brackets.
Make sense, or still confused? :)

anonymous · Answer

would it be (x – 2)^2 + (y + 1)^2 = 64 then?

zepdrix · Answer

Yes, looks good! :)

anonymous · Answer

thank you so much! :)