Chapter 10.4, Problem 35PE

For Exercises 35-42, the equation represents a conic section (nondegenerative case).

a. Use the discriminant to determine the type of conic section represented. (See Example 5)

b. Use a rotation of axes to eliminate the $xy\text{-term}$ to write the equation in the form $A\text{'}x{\text{'}}^2+C\text{'}y{\text{'}}^2+D\text{'}x\text{'}+E\text{'}y\text{'}+F\text{'}=0$ .

c. Write the equation in standard form and sketch the graph.

$3x^2+26\sqrt{3}xy-23y^2-144=0$