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Magazine Problem 4
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{6}{5-5 \cos \theta}$$
Problem 4
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$3 x^{2}+12 x-3 y-9=0$$
Problem 5
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{3}{3+4 \sin \theta}$$
Problem 5
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$6 y^{2}+3 x+18 y-8=0$$
Problem 6
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{6}{2+5 \cos \theta}$$
Problem 6
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$4 x^{2}+5 y^{2}+2 x-y-1=0$$
Problem 7
Identify each conic and sketch its graph. Give the equation of the directrix in rectangular coordinates. $$r=\frac{2}{1-\sin \theta}$$
Problem 8
Identify each conic and sketch its graph. Give the equation of the directrix in rectangular coordinates. $$r=\frac{3}{1-\cos \theta}$$
Problem 9
Identify each conic and sketch its graph. Give the equation of the directrix in rectangular coordinates. $$r=\frac{5}{3+2 \cos \theta}$$
Problem 10
Find the equation of each ellipse described below and sketch its graph. Foci \((-3,0)\) and \((3,0),\) and \(y\) -intercepts \((0,-4)\) and \((0,4)\)
