Conic Sections and Angle Analysis

The video tutorial explains how to write the equation of a rotated conic in standard form by using rotation formulas. It covers the selection of theta based on the cotangent of 2 theta, quadrant considerations, and common mistakes. The tutorial includes a detailed example problem, demonstrating the transformation of the x and y axes and the simplification of the conic equation. The final section focuses on algebraic simplification and graphing the transformed conic.

What is the first step in writing the equation of a rotated conic in standard form?

• Determine the type of conic section.

• Use the equation cot(2θ) = (A - C) / B.

• Graph the conic section.

• Find the center of the conic.

Why do we use rotation formulas in conic sections?

• To simplify the equation and make graphing easier.

• To find the center of the conic.

• To change the type of conic section.

• To eliminate the need for a calculator.

If cot(2θ) is positive, what range should θ be in?

• 90 to 135 degrees

• 45 to 90 degrees

• 135 to 180 degrees

• 0 to 45 degrees

What should you do if you still have an xy term after transformation?

• Check for algebraic mistakes.

• Use a calculator to verify.

• Recalculate the center of the conic.

• Change the type of conic section.

In the first example, what is the value of A?

• 3

• 5

• 8

• 10

What is the angle θ after dividing 2θ by 2 in the example?

• 60 degrees

• 45 degrees

• 30 degrees

• 15 degrees

What type of conic section is identified in the example?

• Circle

• Hyperbola

• Parabola

• Ellipse