SOLUTION: x^2 + y^2 + 4x - 2y = -1 The equation of a circle in the xy-plane is shown above. What is the radius of the circle? A) 2 B) 3 C) 4 D) 9

Algebra ->  Formulas -> SOLUTION: x^2 + y^2 + 4x - 2y = -1 The equation of a circle in the xy-plane is shown above. What is the radius of the circle? A) 2 B) 3 C) 4 D) 9      Log On


   

Question 1046374: x^2 + y^2 + 4x - 2y = -1
The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
A) 2
B) 3
C) 4
D) 9
Found 2 solutions by MathLover1, solver91311:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The equation of a circle in standard form is: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
x%5E2+%2B+y%5E2+%2B+4x+-+2y+=+-1....write it in standard form
%28x%5E2+%2B+4x%29+%2B+%28y%5E2+-+2y%29+=+-1.............complete squares
%28x%5E2+%2B+4x%2Bb%5E2%29+-b%5E2%2B+%28y%5E2+-+2y%2Bb%5E2%29-b%5E2+=+-1
%28x%5E2+%2B+4x%2B2%5E2%29+-2%5E2%2B+%28y%5E2+-+2y%2B1%5E2%29-1%5E2+=+-1
%28x%2B2%29%5E2+-4%2B+%28y+-+1%29%5E2-1+=+-1
%28x%2B2%29%5E2+%2B+%28y+-+1%29%5E2-5+=+-1
%28x%2B2%29%5E2+%2B+%28y+-+1%29%5E2+=+-1%2B5
%28x%2B2%29%5E2+%2B+%28y+-+1%29%5E2+=+4
%28x%2B2%29%5E2+%2B+%28y+-+1%29%5E2+=+2%5E2=> r=2
so, your answer is: A) 2


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Rearrange:



Complete the square on x



Complete the square on y



Collect the constant terms in the RHS



The Right Hand Side is now the Radius SQUARED.

John

My calculator said it, I believe it, that settles it