Problem Set 2 - Math 133 Practice Problems Conics Parametric Equations and Polar Coordinates The following questions are collected from some practice

Problem Set 2 - Math 133 Practice Problems Conics...

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Math 133, Practice Problems: Conics, Parametric Equations and Polar Coordinates The following questions are collected from some practice problems suggested to Math 122 students when they study conics, polar coordinates and parametric equations. 1.Write the equation of the conicx2+ 6x-8y-23 = 0 in standard form, and then findits vertex, focus and the equation of its directrix. (Think about similar questions for ellipsesand hyperbolas where you would find center, vertices, foci, and additionally asymptotes forhyperbolas)2.(a) Find the equation of the hyperbola with foci (2,-6) and (2,4) whose vertices are (2,-4)and (2,2); and find the equation of its asymptotes.(b) Find the equation of ellipse with vertices (-6,2) and (4,2) and foci (-4,2) and (2,2).(c) Sketch the conics you found in (a) and (b). (Think about analogous questions for parabolaswhere one is given, e.g. the focus and vertex).3.(a) Describe the graph whose polar equation isrsinθ= 3. Be specific!(b) Describe the graph whose polar equation isr= 4. Be specific!

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