SOLUTION: Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola . x^2 +4y^2 +2x -24y +33 =0

Question 584869: Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola .
x^2 +4y^2 +2x -24y +33 =0
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola .
x^2 +4y^2 +2x -24y +33 =0
complete the square
(x^2+2x+1)+4(y^2-6y+9)=-33+1+36
(x+1)^2+4(y-3)^2=4
(x+1)^2/4+(y-3)^2=1
This is an equation of an ellipse with horizontal major axis of the standard form:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k) being the (x,y) coordinates of the center
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