Use the Discriminant Test to determine the type of the conic section (in every case non degenerate equation). Plot the curve if you have a computer algebra system.displaystyle{2}{x}{2}-{8}{x}{y}+{3}{y}{2}-{4}={0}

Nann 2020-12-17 Answered

Use the Discriminant Test to determine the type of the conic section (in every case non degenerate equation). Plot the curve if you have a computer algebra system.
2x28xy+3y24=0

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Expert Answer

insonsipthinye
Answered 2020-12-18 Author has 83 answers

Step 1
Given that the equation is 2x28xy+3y24=0
It is known that the general equation of the conic
Ax2+Bxy+Cy2+Dx+Ey+F=0 and the discriminant is given by
Δ=B24AC
If Δ0 then the equation is non degenerate.
B24AC>0, equation represent hyperbola
B24AC=0, equation represent parabola
B24AC<0, equation represent ellipse
Step 2
It's required to find the type of the conic. Here A=2,B=8,C=3.
Δ=B24AC
=(8)24(2)(3)
=6424
=40
>0
Thus, the given equation is hyperbola.
Step 3
Sketch the graph of the equation 2x28xy+3y24=0.
image

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