SOLUTION: Please help me do this problem, graph it, and figure out what it would be. My choices of what it could be are ellipse, circle, parabola, and hyperbola. 9x^2+36y^2-72x-180

Question 435959: Please help me do this problem, graph it, and figure out what it would be. My choices of what it could be are ellipse, circle, parabola, and hyperbola. 9x^2+36y^2-72x-180
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please help me do this problem, graph it, and figure out what it would be. My choices of what it could be are ellipse, circle, parabola, and hyperbola. 9x^2+36y^2-72x-180
..
9x^2+36y^2-72x-180
For an expression to be an equation, it must be equal to some number. I will assume the given expression is equal to zero.
9x^2+36y^2-72x-180=0
9x^2+36y^2-72x=180
completing the squares
9(x^2-8x+16)+36y^2=180-144=36
9(x-4)^2+36y^2=36
divide by 36
(x-4)^2/4+y^2/1=1
Standard form for an ellipse: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b)
with (h,k) being the (x,y) coordinates of the center
At you can see this is an ellipse with center at (4,0) with a horizontal major axis
Also:
a^2=4
a=2
b^2=1
b=1
See the graph below:
..
y=+-(1-(x-4)^2/4)^.5

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