Ask Question
13 May, 07:22

X^2 + Y^2 + ax + 2y + 3 = 0

What number is this equation the equation of a circle?

+5
Answers (1)
  1. 13 May, 07:41
    0
    Eq: (x+a/2) ² + (y+1) ² = (a²-8) / 4

    Center: O (-a/2, - 1)

    Radius: r=0.5*sqrt (a²-8)

    Mandatory: a>2*sqrt (2)

    Step-by-step explanation:

    The circle with center in O (xo, yo) and radius r has the equation:

    (x-xo) ² + (y-yo) ²=r²

    We have:

    x²+y²+ax+2y+3=0

    But: x²+ax=x²+2 (a/2) x+a²/4-a²/4 = (x+a/2) ²-a²/4

    And

    y²+2y+3=y²+2y+1+2 = (y+1) ²+2

    Replacing, we get:

    (x+a/2) ²-a²/4 + (y+1) ²+2=0

    (x+a/2) ² + (y+1) ²=a²/4-2 = (a²-8) / 4

    By visual inspection we note that:

    - center of circle: O (-a/2, - 1)

    - radius: r=sqrt ((a²-8) / 4) = 0.5*sqrt (a²-8). This means a²>8 or a>2*sqrt (2)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “X^2 + Y^2 + ax + 2y + 3 = 0 What number is this equation the equation of a circle? ...” 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