SOLUTION: The type of conic section whose equation is defined by : 4x.x+12x.y+9y.y-52x+26y-81=0

Question 32816: The type of conic section whose equation is defined by :
4x.x+12x.y+9y.y-52x+26y-81=0
Answer by kietra(57) (Show Source): You can put this solution on YOUR website!
First, make sure your equation for a conic section goes along with the general equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. In this case, it is already in that form.
Now, to find out what kind of equation it is, find B^2 - 4AC.
B=12, A=4, C=9 and substitute 12^2 - 4(4)(9) or 144-16(9) = 0
To find out what kind of equation it is, use the following:
If B^2 - 4AC is... then the curve is a...

< 0 ellipse, circle, point or no curve.

= 0 parabola, 2 parallel lines, 1 line or no curve.

> 0 hyperbola or 2 intersecting lines.
In your problem, it equals zero so this is likely a parabola, 2 parallel lines, or 1 line or no curve.

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