Chapter 10.4, Problem 28PE

For Exercises 23-28,

a. Determine an acute angle of rotation to eliminate the $xy\text{-term}$ . (See Example 4)

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. Identify the type of curve represented by the equation.

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

$x^2+2\sqrt{3}xy+3y^2-8\sqrt{3}x+8y=0$