SOLUTION: x^2+4y^2-6x+16y+21=0 ellipse i need help to put it in standard form 9x^2-y^2-72x+8y+119=0 hyperbola standard form

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Question 874612: x^2+4y^2-6x+16y+21=0 ellipse i need help to put it in standard form
9x^2-y^2-72x+8y+119=0 hyperbola standard form
Answer by lwsshak3(11628) About Me  (Show Source):
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x^2+4y^2-6x+16y+21=0 ellipse i need help to put it in standard form
9x^2-y^2-72x+8y+119=0 hyperbola standard form
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x^2+4y^2-6x+16y+21=0
x^2-6x+4y^2+16y=-21
complete the square:
(x^2-6x+9)+4(y^2+4y+4)=-21+9+16
(x-3)^2+4(y+2)^2=4
divide by 4
(x-3)^2/4+(y+2)^2=1
This is an equation of an ellipse with horizontal major axis and center at (3,-2)
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1, a>b, (h,k)=coordinates of center
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9x^2-y^2-72x+8y+119=0
9x^2-72x-y^2+8y=-119
complete the square:
9(x^2-8x+16)-(y^2-8y+16)=-119+144-16
9(x-4)^2-(y-4)^2=9
divide by 9
(x-4)^2-(y-4)^2/9=1
This is an equation of a hyperbola with horizontal transverse axis and center at (4,4)
Its standard form of equation: %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1, (h,k)=coordinates of center