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Hawki5

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conic sections puzzler

I am stumped on a conic sections problem.
I am fouling up the algebra somehow, so I\\\'m not getting the same radius as the book I am working from. Here is the original problem:

x^2 + y^2 + 4y + 2x - 20 = 0

The book says I should get to the following step in the process of completing the square:

x^2 + y^2 - 4y + 2y - 4 = 0

But I just don\\\'t see where the -4y or the - 4 is coming from.

I get the following next step instead:

(x^2 + 2x + 1) + (y^2 - 4y + 4) = 20 + 1 + 4

This takes me to:

(x + 1)^2 + (y - 2)^2 = 25

then,

25 = r^2
so r = 5

But, I should be coming up with r = 3

Help!

746 day(s) ago

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Answers (3)


x^2 + y^2 + 4y + 2x - 20 = 0
(x^2 +2x +1)+ ( y^2 + 4y ++4) =20+1+4
(x+1)^2+(y+2)^2 =(5)^2

the centre are (-1, - 2) and radius = 5 units

Posted 745 dy ago

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jcatta21
Similar to the above response, the conic can be simplified via the completing square method.

x^2 + y^2 + 4y + 2x - 20 = 0 => x^2 + 2x + y^2 - 20 = 0 => (x + 2)^2 + (y + 2)^2 = 25=> Circle.

J.C

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matherapist
I sort of agree with your analysis. It's completing the square.

I don't understand x^2 + y^2 - 4y + 2y - 4 = 0 eitherthough it looks like a copy error in the 2y term (2x??)

Completing the square of x^2 + y^2 + 4y + 2x - 20 = 0 (orig problem) gives

x^2 + y^2 + 4y + 2x +4+1= 20+4 +1 or (x+1)^2+(y+2)^2=25

Sometimes books have errors so don't sweat this




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