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JoAnne JoAnne
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10 years ago
Find the center, vertices, and foci of the ellipse with equation  3x2 + 4y2 +12x – 8y – 32 = 0.
Source  Precalculus (A Unit Circle Approach) - Analytic Geometry
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Joanne

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#1
Donated
10 years ago
3x^2+12x+4y^2-8y=32
3(x^2+4x)+4(y^2-2y)=32
3(x^2+4x+4)-12+4(y^2-2y+1)-4=32 (Complete the square for x and y)
3(x+2)^2+4(y-1)^2-16=32
3(x+2)^2+4(y-1)^2=48
((3(x+2)^2)/48)+((4(y-1)^2)/48)=48/48
(((x+2)^2)/16)+(((y-1)^2)/12)=1 (standard form)

Center= (-2,1)
Vertices= (2,1) and (-6,1)
Foci= (0,1) and (-4,1)
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#2
Staff Member
10 years ago
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