Question

How does your strategy presented in Problem 59 change if the equation is of the following form:

$A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0$

Short answer

The strategy changed to rotation of axes.

Step-by-step solution

Step 1. Given Information

The given equation is $A{x}^2+Bxy+C{y}^2+Dx+Ey+F=0---\left(1\right)$

We are given equation, we are asked to change our strategy from the previous problem.

Step 2. Previous Strategy

As this is already discussed the procedure for identifying the graph of such type of equation. So, complete the squares of the quadratic expressions in x or y, or both.

Step 3. New Strategy

Now, let's take attention to the equations in the form of equation (1), where$B\ne 0$.

In the rotation of axes, the origin remains fixed while the x-axis and y-axis are rotated through an angle u to a new position and the new positions of the x-axis and the y-axis are denoted by $x\text{'}$and $y\text{'}$, respectively,