Exam 10: Parametric and Polar Curves; Conic Sections

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?

For the parametric curve: x = 3t + 8, y = 12t + 9, eliminate the parameter and express in rectangular form.

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

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

For the parametric equation x = 9t² + 11 , y = 6t³ - 12 , the value of at t = 1 is

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

For the parametric curve: , y = 6t² - 10, eliminate the parameter and express in rectangular form.

The vertex of the parabola is

Find the vertex of the parabola in the x'y'-coordinate system.

What are the polar coordinates of a point whose rectangular coordinates are given as ?

Find the inverse of the parametric equation x = 6t² - 2t + 7 , y = 6t - 5

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

Graph the parametric equation x = 2t³ , y = 4t² .

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

The area of the region bounded by the curve is

Find the equation of the ellipse with foci and such that the distances from the foci to any point on the ellipse sum to 34.

Find all points on the circle where the tangent line is horizontal.

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

Find the center of the hyperbola in the xy-coordinate system.