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. 2x2−8xy+3y2−4=0

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insonsipthinye · Accepted Answer

Step 1 Given that the equation is 2x2−8xy+3y2−4=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=B2−4AC If Δ≠0 then the equation is non degenerate. B2−4AC&amp;gt;0, equation represent hyperbola B2−4AC=0, equation represent parabola B2−4AC&amp;lt;0, equation represent ellipse Step 2 It&#039;s required to find the type of the conic. Here A=2,B=−8,C=3. Δ=B2−4AC =(−8)2−4(2)(3) =64−24 =40 &amp;gt;0 Thus, the given equation is hyperbola. Step 3 Sketch the graph of the equation 2x2−8xy+3y2−4=0.

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}

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