Chapter 10.4, Problem 42PE

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.

$7x^2+50xy+7y^2+78\sqrt{2}x+114\sqrt{2}y-18=0$