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Find a degree 
Magazine Problem 6
Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph. $$\frac{(x-3)^{2}}{16}+(y+3)^{2}=1$$
Problem 6
Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions. Ellipse, eccentricity \(\frac{1}{2}, \operatorname{directrix} y=-4\)
Problem 7
Determine the \(X Y\)-coordinates of the given point if the coordinate axes are rotated through the indicated angle. $$(0,2), \quad \phi=55^{\circ}$$
Problem 7
Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph. $$\frac{x^{2}}{9}+\frac{(y+5)^{2}}{25}=1$$
Problem 7
Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions. Hyperbola, eccentricity \(4,\) directrix \(r=5 \sec \theta\)
Problem 8
Find the center, foci, and vertices of the ellipse, and determine the lengths of the major and minor axes. Then sketch the graph. $$\frac{(x+2)^{2}}{4}+y^{2}=1$$
Problem 8
Determine the \(X Y\)-coordinates of the given point if the coordinate axes are rotated through the indicated angle. $$(\sqrt{2}, 4 \sqrt{2}), \quad \phi=45^{\circ}$$
Problem 8
Write a polar equation of a conic that has its focus at the origin and satisfies the given conditions. Ellipse, eccentricity \(0.6,\) directrix \(r=2 \csc \theta\)
Problem 9
Find the vertices, foci, and eccentricity of the ellipse. Determine the lengths of the major and minor axes, and sketch the graph. $$\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$$
Problem 9
Determine the equation of the given conic in \(X Y\)-coordinates when the coordinate axes are rotated through the indicated angle. $$x^{2}-3 y^{2}=4, \quad \phi=60^{\circ}$$
