Exam 6: Topics-In-Analytic-Geometry

The path of a projectile projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is .In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels.A ball is thrown from the top of a 150-foot tower with a velocity of 32 feet per second.Find the equation of the parabolic path. ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentrity Directrix Parabola ​ ​

Find the inclination Θ (in degrees) of the line with a slope of m.Round your answer to one decimal places. ​ ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. ​ ​

Find a polar equation of the conic with its focus at the pole. ​ Conics Eccentricity Directrix Hyperbola ​

Determine the angle through which the axes are rotated.Round your answer to two decimal places. ​ ​

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​ Vertices: ; Foci: ​

Find the distance between the point and the line.Round your answer to four decimal places. ​ ​

Convert the rectangular equation to polar form.Assume r > 1. ​ ​

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​ ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus:

Select the graph of degenerate conic. ​ ​

Select the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. ​ ​

Select the standard form of the equation of the parabola and determine the coordinates of the focus. ​ ​

Find the vertices and asymptotes of the hyperbola. ​

Find the center and vertices which located on the major axis of the ellipse.

Use a graphing utility to graph the conic. ​ ​

Find the standard form of the equation of the parabola with the given characteristics. ​ Vertex: ; directrix: ​

Use the discriminant to classify the graph. ​ ​

Select the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. ​ ​