Exam 10: Parametric and Polar Curves; Conic Sections

Find the equation of the ellipse with a major axis length of , a minor axis length of , center at (0, 0), and foci on the y-axis.

Find the equation for the given graph when A = 6

Find the equation of the hyperbola with vertices and asymptotes .

Find the approximate arc length of x = 3t + 2 , y = 4t - 6 , over the interval .

Sketch the parabola x²- 10x - 2y 13 = 0 showing the focus, vertex and directrix.

For the parametric curve: x = 3 cos 5t, y = 3 sin 5t, eliminate the parameter and express in rectangular form.

Find the area of one pedal of the rose .

Find the equation for the parabola whose directrix is x = 6 and vertex at (9, 6). Where is the focus located?

Find the equation of the curve described. The ellipse with a major axis length of , a minor axis of , center at (0, 0), and foci on the x-axis.

Find the area inside the circle and outside the cardioid .

For the parametric curve: x = 6t², y = 72t⁴ + 18t², eliminate the parameter and express in rectangular form.

Identify the conic section represented by .

Find the area of the region outside the circle and inside the graph of .

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

Find at the point where if

Identify the conic section represented by .

Find the distance between the pole and the vertices for the conic that has its focus at the pole and its directrix is units above the pole and its eccentricity is .

Find the equation of the parabola with focus at (6, -1) and directrix x = 2. Sketch.

Sketch the curve in polar coordinates.

State the name that describes the polar curve most precisely.