Exam 6: Topics-In-Analytic-Geometry

The -coordinate system has been rotated degrees from the -coordinate system.The coordinates of a point in the -coordinate system are given.Find the coordinates of the point in the rotated coordinate system. ​ , ​

Use a graphing utility to graph the parabola. ​ ​

Find the inclination (in radians and degrees) of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​ ​

A point in polar coordinates is given.Convert the point to rectangular coordinates.Round your answers to one decimal places. ​ ​

Find the eccentricity of the ellipse. ​ ​

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

The Halley's Comet has an elliptical orbit with an eccentricity of .The length of the major axis of the orbit is approximately 35.1 astronomical units.Find a polar equation for the orbit.How close does the comet come to the sun? ​

Select the graph of the equation. ​ ​

Identify the conic and select its correct graph. ​ ​

The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957).Its highest point above Earths surface was 943 kilometers, and its lowest point was 211 kilometers (see figure).The center of Earth was at one focus of the elliptical orbit, and the radius of Earth is 6392 kilometers.Find the eccentricity of the orbit.Round your results to four decimal place. ​ ​ ​

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

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

Find the center and vertices of the hyperbola and sketch its graph, using asymptotes as sketching aids. ​ ​

Use a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates, r > 0.Round your answers to three decimal places. ​ ​

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Find the standard form of the equation of the ellipse with the given characteristics. ​ Vertices: ; minor axis of length 10. ​

Convert the polar equation to rectangular form. ​ ​

Find a set of parametric equations for the rectangular equation. ​ ​

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-7, -9) directrix:

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