Find the equation of an ellipse by eliminating the parameter of parametric equations

The video tutorial explains how to eliminate the parameter Theta from two given equations using the Pythagorean identity. The instructor demonstrates solving for sine and cosine of Theta, forming an equation with squared terms, and identifying the resulting shape as an ellipse rather than a circle. The tutorial concludes with a preview of the next chapter.

What is the primary goal when dealing with the given parametric equations in this lesson?

• To find the value of Theta

• To eliminate the parameter Theta

• To solve for X and Y directly

• To graph the equations

Which identity is used to eliminate the parameter Theta in the equations?

• Sine squared plus cosine squared equals one

• Tangent squared plus one equals secant squared

• Sine of double angle equals two sine cosine

• Cosine of double angle equals cosine squared minus sine squared

What is the form of the equation after substituting sine and cosine expressions?

• A cubic equation

• An equation in the form of X-H squared plus Y-K squared

• A quadratic equation

• A linear equation

Why is the resulting shape not a perfect circle?

• The values of X and Y are too large

• The equation is not in standard form

• The coefficients of X and Y are not equal

• The parameter Theta was not eliminated correctly

What mathematical shape does the equation represent after transformation?

• A parabola

• An ellipse

• A hyperbola

• A circle