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Magazine Problem 53
Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-5 ; e=\frac{3}{4}\)
Problem 53
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-5 ; e=\frac{3}{4}\)
Problem 53
For the following exercises, determine the angle of rotation in order to eliminate the xy term. Then graph the new set of axes. $$4 x^{2}+6 \sqrt{3} x y+10 y^{2}+20 x-40 y=0$$
Problem 54
For the following exercises, determine the angle of rotation in order to eliminate the xy term. Then graph the new set of axes. $$8 x^{2}+3 x y+4 y^{2}+2 x-4=0$$
Problem 54
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=2 ; e=2.5\)
Problem 54
Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(y=2 ; e=2.5\)
Problem 55
For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-3 ; e=\frac{1}{3}\)
Problem 55
Find the polar equation of the conic with focus at the origin and the given eccentricity and directrix. Directrix: \(x=-3 ; e=\frac{1}{3}\)
Problem 55
For the following exercises, determine the angle of rotation in order to eliminate the xy term. Then graph the new set of axes. $$16 x^{2}+24 x y+9 y^{2}+20 x-44 y=0$$
Problem 56
Express each equation in polar form with \(r\) as a function of \(\theta\). $$ x y=2 $$
