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Magazine Problem 36
Convert each polar equation to a rectangular equation. \(r=\frac{3 \csc \theta}{\csc \theta-1}\)
Problem 36
Find an equation for each ellipse. Graph the equation. Vertices at (卤4,0)\(; \quad y\) -intercepts are 卤1
Problem 36
Find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation. \(2 x^{2}-y^{2}=4\)
Problem 37
Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Focus at (-3,-2)\(;\) directrix the line \(x=1\)
Problem 37
In Problems 37-42, find a polar equation for each conic. For each, a focus is at the pole. \(e=1 ;\) directrix is parallel to the polar axis, 1 unit above the pole.
Problem 37
Find an equation for each ellipse. Graph the equation. Center at (0,0)\(;\) vertex at (0,4)\(; \quad b=1\)
Problem 38
Find a polar equation for each conic. For each, a focus is at the pole. \(e=1 ;\) directrix is parallel to the polar axis, 2 units below the pole.
Problem 38
Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Focus at (-4,4)\(;\) directrix the line \(y=-2\)
Problem 39
Find the vertex, focus, and directrix of each parabola. Graph the equation. \(x^{2}=4 y\)
Problem 39
In Problems 39-42, find parametric equations for an object that moves along the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) with the motion described. The motion begins at \((2,0),\) is clockwise, and requires 2 seconds for a complete revolution.
