Question 660534: What do they mean when they say "Write the equation of a circle with radius equal to square root 2 and center at (2, 5)." I understand how to set up the equations but what's throwing me off is the radius equal to square root 2. What does that mean?
Found 2 solutions by stanbon, math-vortex:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What do they mean when they say "Write the equation of a circle with radius equal to square root 2 and center at (2, 5)." I understand how to set up the equations but what's throwing me off is the radius equal to square root 2. What does that mean?
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Ans: (x-2)^2 + (y-5)^2 = (sqrt(2))^2
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Cheers,
Stan H.
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website! Hi, there---
Hi, there--
The formula for the equation of a circle is (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle, and r is the radius.
A circle can have a radius of sqrt(2). It's an irrational length so you cannot measure it exactly
with a rule, but it is a valid mathematical length.
When you plug r=sqrt(2) into your equation formula, you will get
(x-h)^2 + (y-k)^2 = (sqrt(2))^2
Squaring a number is the reciprocal operation to taking the square root; they undo each other.
Therefore, the square root of 2 squared is just 2.
Insert (h,k)=(2,5), your equation is
(x-2)^2 + (y-5)^2 = 2
Mrs. Figgy
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