Determine whether the statement If D≠0orE≠0, then the graph of y2−x2+Dx+Ey=0 is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

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Determine whether the statement If D≠0orE≠0,   then the graph of y2−x2+Dx+Ey=0 is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

estenutC · Accepted Answer

Step 1 We have given a statement: If D≠0orE≠0, then graph of y2−x2+Dx+Ey=0 is a hyperbolais. Step 2 We know the general form of conic section: Ax2+Bxy+Cy2+Dx+Ey+F=0 To find the type of conic section we solve for B2−4AC: (i) If B2−4AC&amp;lt;0 then the conic section is ellipse. (ii) If B2−4AC&amp;lt;0andA=C,B=0 then we have a perfect circle. (iii) If B2−4AC=0, then we have a parabola. B2−4AC&amp;gt;0, then we have a hyperbola Hyperbola defined as: (x−h)2a2+(y−k)2b2=1 Where (h, k) are center. When E,D=0,then(h,k)=(0,0) Then the center will be at (0,0) Step 3 Hence, the given statement is incorrect since the given condition is not mandatory for a conic section to be a hyperbola.

Determine whether the statement If displaystyle{D}ne{0}{quadtext{or}quad}{E}ne{0}, then the graph of displaystyle{y}^{2}-{x}^{2}+{D}{x}+{E}{y}={0} is a hyperbolais true or false. If it is false, explain why or give an example that shows it is false.

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