SOLUTION: 2x^2+3x+6y^2-2y-5=0 circle ellipse parabola or hyperbola ???

Question 197363: 2x^2+3x+6y^2-2y-5=0
circle ellipse parabola or hyperbola
???
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
2x^2+3x+6y^2-2y-5=0

2x^2+3x+6y^2-2y=5

2(x^2+3/2x)+6(y^2-1/3y)=5

2(x^2+3/2x+9/16)+6(y^2-1/3y)=5+9/8

2(x^2+3/2x+9/16)+6(y^2-1/3y+1/36)=5+9/8+1/6

2(x+3/4)^2+6(y-1/6)^2=151/24

[ (x+3/4)^2 ]/(48/151) + [ 6(y-1/6)^2 ]/(144/151)=1

Eqn fits form : (x-h)^2/a^2 + (y-k)^2/b^2 = 1 (ellipse)

Ans:2x^2+3x+6y^2-2y-5=0 is ellipse
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