SOLUTION: 3. Identify the conic section by writing 4x^2 + 4y^2 + 40x + 16y + 40 = 0 in standard form. (Please show how and why.) PS. Thank you in advance!!

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 3. Identify the conic section by writing 4x^2 + 4y^2 + 40x + 16y + 40 = 0 in standard form. (Please show how and why.) PS. Thank you in advance!!      Log On


   

Question 1091494: 3. Identify the conic section by writing 4x^2 + 4y^2 + 40x + 16y + 40 = 0 in standard form. (Please show how and why.)
PS. Thank you in advance!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Identify the conic section by writing 4x^2 + 4y^2 + 40x + 16y + 40 = 0 in standard form.
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It's not necessary to write it in standard form.
Both x & y have squared terms with the same coefficient (and no x*y term) --> a circle.
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4x^2 + 4y^2 + 40x + 16y + 40 = 0
Divide by 4
x^2 + y^2 + 10x + 4y + 10 = 0
x^2 + 10x + y^2 + 4y = -10
Complete the squares for x & y
x^2 + 10x + 25 + y^2 + 4y + 4 = -10 + 25 + 4 = 19
(x+5)^2 + (y+2)^2 = 19
A circle: center at (-5,-2), r = sqrt(19)