SOLUTION: Determine the conic: 9x^2 + 2y^2 + 100y - 72x + 19 = 0, give its properties and sketch the graph

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Question 969561: Determine the conic: 9x^2 + 2y^2 + 100y - 72x + 19 = 0, give its properties and sketch the graph
Answer by lwsshak3(11628) About Me  (Show Source):
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Determine the conic: 9x^2 + 2y^2 + 100y - 72x + 19 = 0, give its properties and sketch the graph.
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9x^2- 72x + 2y^2 + 100y + 19 = 0
complete the square:
9(x^2-8x+16) + 2(y^2+50y+625) =-19+144+1350
9(x-4)^2+2(y+25)^2=1475
equation of given ellipse:%28x-4%29%5E2%2F%281475%2F9%29%2B%28y%2B25%29%5E2%2F%281475%2F2%29=1
This is an equation of an ellipse with vertical major axis.
Ita standard form of equation: %28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1, a>b, (h,k)=coordinates of center.
For given ellipse:
center: (4, -25)
a^2=1475/2
a=√(1475/2)≈27.2 (distance from center to vertices)
b^2=1475/9
b=√(1479/9)≈12.8 (distance from center to co-vertices)
see graph below: