SOLUTION: how do you find the radius of the circle x^2+y^2-2x+4y=4?
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Question 385641: how do you find the radius of the circle x^2+y^2-2x+4y=4?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Complete the square on each of the variables:
Group variable types:
\ +\ \left(y^2\ +\ 4y\right)\ =\ 4)
Start with the x term. Divide the coefficient by 2, square the result, add the squared result to both sides of the equation. -2 divided by 2 is -1, -1 squared is 1, add 1 to both sides:
\ +\ \left(y^2\ +\ 4y\right)\ =\ 4\ +\ 1)
Repeat the process for y:
\ +\ \left(y^2\ +\ 4y\ +\ 4\right)\ =\ 4\ +\ 1\ +\ 4)
Factor the two perfect square trinomials in the LHS and collect the constants in the RHS:
^2\ +\ \left(y\ +\ 2\right)^2\ =\ 9)
The constant term in the RHS is now the radius squared. The radius is the positive square root of the constant.
John
My calculator said it, I believe it, that settles it
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