91Ó°ÊÓ

In Exercises 43-50, (a) use the discriminant to classify the graph, (b) use the Quadratic Formula to solve for \(y\), and (c) use a graphing utility to graph the equation. \(16x^2-8xy+y^2-10x+5y=0\)

In Exercises 29-52, identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(x^2+y^2-2x+4y-31=0\)

In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Hyperbola \(\textit{Eccentricity}\) \(e=2\) \(\textit{Directrix}\) \(x=1\)

In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Hyperbola \(\textit{Eccentricity}\) \(e=\frac{3}{2}\) \(\textit{Directrix}\) \(x=-1\)

In Exercises 29-52, identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(x^2+5y^2-8x-30y-39=0\)

In Exercises 41-48, find a set of parametric equations for the rectangular equation using (a) \(t=x\) and (b) \(t=2-x\). \(y=x^2+1\)

In Exercises 37-46, find the angle \(\theta\) (in radians and degrees)between the lines. \(3x - 5y = 3\) \(3x + 5y = 12\)

In Exercises 43-50, (a) use the discriminant to classify the graph, (b) use the Quadratic Formula to solve for \(y\), and (c) use a graphing utility to graph the equation. \(x^2-4xy-2y^2-6=0\)

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(0, 5\right)\)

In Exercises 33-46, find the vertex, focus, and directrix of the parabola, and sketch its graph. \(x=\frac{1}{4}(y^2 + 2y + 33)\)