This figure shows concentric circles of radii 3 and 5, respectively, centered at the origin of an xy-coordinate system. A ray from the center at an angle of t degrees to the x-axis cuts the two circles at points A and B. From A, a vertical line is drawn; and from B, a horizontal line is drawn. These two lines intersect at point P on an ellipse.

Question

This figure shows concentric circles of radii 3 and 5, respectively, centered at the origin of an xy-coordinate system.  A ray from the center at an angle of t degrees to the x-axis cuts the two circles at points A and B.  From A, a vertical line is drawn; and from B, a horizontal line is drawn.  These two lines intersect at point P on an ellipse.

For the value of t shown, draw a right triangle (on your paper) for which one of the legs equals the x-coordinate of point P.  Use the result to write an equation for x as a function of t.

For the value of t shown, draw a right triangle (on your paper) for which one of the legs equals the y-coordinate of point P.  Use the result to write an equation for y as a function of t.

Diagram can be found blondebeliever.tumblr.[com]/precalc (on my blog) under question 2!

Steve · Answer

x = 5cos(t) y = 3sin(t)