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Magazine Problem 57
Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Exercises \(57-68 .\) $$ x^{2}+4 x+y^{2}=12 $$
Problem 57
Replace the Cartesian equations in Exercises \(53-66\) with equivalent polar equations. $$x^{2}+y^{2}=4$$
Problem 58
Find polar equations for the circles in Exercises \(57-64 .\) Sketch each circle in the coordinate plane and label it with both its Cartesian and polar equations. $$(x+2)^{2}+y^{2}=4$$
Problem 58
Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Exercises \(57-68 .\) $$ 2 x^{2}+2 y^{2}-28 x+12 y+114=0 $$
Problem 59
Replace the Cartesian equations in Exercises \(53-66\) with equivalent polar equations. $$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$
Problem 59
Find polar equations for the circles in Exercises \(57-64 .\) Sketch each circle in the coordinate plane and label it with both its Cartesian and polar equations. $$x^{2}+(y-5)^{2}=25$$
Problem 60
Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Exercises \(57-68 .\) $$ y^{2}-4 y-8 x-12=0 $$
Problem 61
Find polar equations for the circles in Exercises \(57-64 .\) Sketch each circle in the coordinate plane and label it with both its Cartesian and polar equations. $$x^{2}+2 x+y^{2}=0$$
Problem 61
Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in Exercises \(57-68 .\) $$ x^{2}+5 y^{2}+4 x=1 $$
Problem 62
Replace the Cartesian equations in Exercises \(53-66\) with equivalent polar equations. $$x^{2}+x y+y^{2}=1$$
