In this lesson, we will learn how to write the standard form of the equations of conic sections with rotated axes that are no longer parallel to the coordinate axes.

Q1:

Consider the conic equation 𝑥𝑦−11=0. If the conic is rotated to eliminate the 𝑥𝑦-term, what will the new equation be in standard form?

Q2:

Consider the conic equation 𝑥−𝑥𝑦+𝑦−3=0.

What is the type of conic?

If the conic is rotated to eliminate the 𝑥𝑦-term, what will the new equation be in standard form?

Which of the following is the sketch of the curve?

Q3:

Consider the conic equation 2𝑥+√3𝑥𝑦+𝑦=2.

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