The type of the conic section using the Discriminant Test and plot the curve using a computer algebra system. x2 − 2xy + y2 + 24x − 8=0

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The type of the conic section using the Discriminant Test and plot the curve using a computer algebra system. x2 − 2xy + y2 + 24x − 8=0

diskusje5 · Accepted Answer

Concept Used: The general equation of conic ax2 + 2hxy + by2 + 2gx + 2fy + c=0 has the discriminant Δ and its given as Δ=∣ahghbfgfc∣=abc + 2fgh − af2 − bg2 − ch2 The general equation of conic ax2 + 2hxy + by2 + 2gx + 2fy + c=0 can also be written in the following way Ax2 + BXY + Cy2 + Dx + Ey + F=0 If Δ≠q0, then the equation is nondegenerate and under this case var¬h∈g If B2 − 4AC &amp;gt; 0, it represents a hyperbola and a rectangular hyperbola if (A + C=0) var¬h∈g If B2 − 4AC=0, it represents a parabola. var¬h∈g If B2 − 4AC &amp;lt; 0,it represents a circle (A=C, B=0) or ellipse A≠qC Calculations: The given equation is: x2 − 2xy + y2 + 24x − 8=0 and the equation is nondegenerate, hence Δ≠q0. Now let&#039;s find the value of B2 − 4AC. From the given equation we have A=1, B= −2, C=1, so on substitution we get ⇒ B2 − 4AC=(−2)2 − 4 ⋅ 1 ⋅ 1 ⇒ B2 − 4AC=4 − 4 ⇒ B2 − 4AC=0 Hence the given equation represents a Parabola. The plot of the given curve is as below:  Conclusion: The given equation represents a Parabola and the plot is shown above.

The type of the conic section using the Discriminant Test and plot the curve using a computer algebra system.x2 - 2xy + y2 + 24x - 8=0

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