Ask Question
20 December, 19:28

X 2 + y 2 + 4x-2y=-1space, x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, plus, 4, x, minus, 2, y, equals, minus, 1 the equation of a circle in the xyxyx, y-plane is shown above. what is the radius of the circle? choose 1 answer: (choice

a. a 2

+4
Answers (1)
  1. 20 December, 19:30
    0
    The radius is 2.

    We will rewrite this equation in center-radius form,

    (x-h) ² + (y-k²) = r²

    where (h, k) is the center of the circle and r is the radius.

    In order to do this, we will need to complete the square. We will first rewrite this with the x terms grouped together and the y terms grouped together:

    x²+4x+y²-2y = - 1

    To complete the square for the x terms, we divide the coefficient b (as in bx) by 2:

    4/2 = 2

    Now we square this:

    2²=4

    We will add this to both sides of the equation (in order to maintain balance, we must add it to both sides):

    x²+4x+4+y²-2y=-1+4

    x²+4x+4+y²-2y=3

    We have completed the square for the x terms. When we divided b by 2, that gave us the number we need, 2:

    (x+2) ²+y²-2y=3

    Now we will do the same thing for the y terms. The b for our y terms is - 2:

    -2/2 = - 1

    (-1) ²=1

    So we will add 1 to both sides, and use - 1 in the finalized form:

    (x+2) ²+y²-2y+1=3+1

    (x+2) ² + (y-1) ²=4

    We can see that the center would be located at (-2, 1) and the radius is √4=2.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “X 2 + y 2 + 4x-2y=-1space, x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, plus, 4, x, minus, 2, ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers