SOLUTION: A diameter of a circle has endpoints at (-1,3) and (-1,-3) Find the area of the circle and please also graph it.

Algebra ->  Circles -> SOLUTION: A diameter of a circle has endpoints at (-1,3) and (-1,-3) Find the area of the circle and please also graph it.      Log On


   

Question 197618: A diameter of a circle has endpoints at (-1,3) and (-1,-3) Find the area of the circle and please also graph it.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
From the given coordinates of the end points of the diameter, (-1,3) and (-1,-3), you can see that the diameter is 6 units.
This was found by:
D+=+y%5B2%5D-y%5B1%5D Substituting y%5B1%5D+=+3 and y%5B2%5D+=+-3, we get:
D+=+-3-3
D+=+6 so the radius, r+=+3
The area of a circle is found by:
A+=+pi%2Ar%5E2 Substituting pi+=+3.14 and r+=+3 we get:
A+=+%283.14%29%283%5E2%29
A+=+%283.14%29%289%29
highlight%28A+=+28.26%29sq. units.
To graph the circle, you first need to find the equation of the circle.
Using the standard form for a circle with center at (h,k) and radius r:
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 Substitute r = 3.
The center of this circle is located at (-1, 0), so making the appropriate substitutions, we get:
%28x-%28-1%29%29%5E2%2B%28y-0%29+=+3%5E2 Simplifying, we have:
%28x%2B1%29%5E2%2B%28y%29%5E2+=+9
Now to graph this circle, you have to solve this equation for y and then graph the two solutions on the same coordinate plane.
Solving for y:
%28x%2B1%29%5E2%2By%5E2+=+9 Subtract %28x%2B1%29%5E2from both sides.
y%5E2+=+-%28x%2B1%29%5E2%2B9 Expand the right side.
y%5E2+=+-%28x%5E2%2B2x%2B1%29%2B9
y%5E2+=+-x%5E2-2x%2B8 Now take the square root of both sides to get:
y+=+sqrt%28-x%5E2-2x%2B8%29 and y+=+-sqrt%28-x%5E2-2x%2B8%29
Now we can graph these two solutions:
graph%28400%2C400%2C-5%2C5%2C-5%2C5%2Csqrt%28-x%5E2-2x%2B8%29%2C-sqrt%28-x%5E2-2x%2B8%29%29