standard form: please check if I did it right!!

K

kathy's

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Dec 20, 2005
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Write the equation 9x^2 + 4y^2 + 18x - 16y - 11 = 0 in standrad form.

My work:

. . .9x^2 + 4y^2 + 18x - 16y - 11 = 0

. . .(9x^2 + 18x) + (4y^2 - 16y) = 11

. . .9(x^2 + 2x) + 4(y^2 - 4y) = 11

. . .9(x^2 + 2x + 1) - 9(1) + 4(y^2 - 4y + 4) - 4(4) = 11

. . .9(x + 1)^2 - 9 + 4(y - 2)^2 - 16 = 11

. . .9(x + 1)^2 + 4(y - 2)^2 - 25 = 11

. . .9(x + 1)^2 + 4(y - 2)^2 - 25 + 25 = 11 + 25

. . .9(x + 1)^2 + 4(y - 2)^2 = 36

Dividing by 36, I get:

. . .[(x + 1)^2] / 4 + [(y - 2)^2] / 9 = 1

So my answer is:

. . .[(x + 1)^2] / 4 + [(y - 2)^2] / 9 = 1

Thank you for checking my work!!! :)
 
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