Exam 10: Parametric and Polar Curves; Conic Sections

Find the center of the ellipse in the x'y'-coordinate system.

Sketch the parabola y² - 4y- 7x + 11 = 0 showing the focus, vertex, and directrix.

Identify the type of conic section by transforming to rectangular coordinates.

Rotate the coordinate axes to remove the xy-term. What is the equation in the new coordinate system? What type of conic section is it?

Find approximations for the intersection point(s) of the cardioid and the cardioid for . Round your answer to six decimal places.

What are the polar coordinates of a point whose rectangular coordinates are given as ?Note: n is an integer.

Find the area inside the circle and outside the cardioid .

Find the ends of the major axis of the ellipse in the x'y'-coordinate system.

For the parametric curve: x = 6t, y = 108t², eliminate the parameter and express in rectangular form.

Rotate the coordinates to remove the xy-term. Then, name the conic.

For the parametric curve: , y = 3t² - 8, eliminate the parameter and express in rectangular form.

Graph the parametric equation x = 2t cos t , y = 3t sin t .

Find the slope of the tangent to the curve at the point where .

Identify the conic section represented by .

Find the area of the region enclosed by .

Convert the following equation to polar coordinates.

Find the equation of the tangent to the curve and at .

Rotate the coordinates to remove the xy-term. Then, name the conic.

Determine the rotation angle that will eliminate the xy-term.

Express the given curve in polar coordinates.