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

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) (Show Source): You can put this solution on YOUR website!
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: , a>b, (h,k)=coordinates of center
..
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: , (h,k)=coordinates of center

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