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Chapter 6: Problem 3
To plot the point \((r, \theta),\) use the __________ coordinate system.
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Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (卤5,0)\(;\) major axis of length 14
Sketch the graph of the ellipse, using latera recta. \(\frac{x^{2}}{4}+\frac{y^{2}}{1}=1\)
A line segment through a focus of an ellipse with endpoints on the ellipse and perpendicular to the major axis is called a latus rectum of the ellipse. Therefore, an ellipse has two latera recta. Knowing the length of the latera recta is helpful in sketching an ellipse because it yields other points on the curve (see figure). Show that the length of each latus rectum is \(2 b^{2} / a\)
Find the standard form of the equation of the parabola with the given characteristics. Vertex: (4,3)\(;\) focus: (6,3)
Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)
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