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Question 813417: Determine the type of curve represented by the equation. Find the foci and vertices (if any) Gary is x years old today. two years ago, his grandfather was 3 times older than Gary at that time.
2x^2-12x+y^2+6y+26=0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Determine the type of curve represented by the equation. Find the foci and vertices (if any)::
2x^2-12x+y^2+6y+26 = 0
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2(x^2-6x+9) + (y^2+6y+9) = -26+18+9
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2(x-3)^2 + (y+3)^2 = 1
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(x-3)^2/(1/2) + (y+3)^2/1 = 1
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Ellipse with center at (3,-3)
a = sqrt(1) = 1 ; b = sqrt(1/2) = sqrt(2)/2
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a^2 = b^2+c^2
c = sqrt[1-1/2] = sqrt(2)/2
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Foci:(h, k+-c)
Foci:: (3 ,-3-(sqrt(2)/2) and (3, -3+(sqrt(2)/2))
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Cheers,
Stan H.
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