91Ó°ÊÓ

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(-4, -3\right)\)

In Exercises 23-48, sketch the graph of the polar equation using symmetry, zeros, maximum \(r\)-values, and any other additional points. \(r= \dfrac{6}{2\ \sin\ \theta -\ 3\ \cos\ \theta}\)

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. \(6x^2+2y^2+18x-10y+2=0\)

In Exercises 37-46, find the angle \(\theta\) (in radians and degrees)between the lines. \(0.02x - 0.05y = -0.19\) \(0.03x + 0.04y = 0.52\)

In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Parabola \(\textit{Vertex or Vertices}\) \((8, 0)\)

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

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. \(x^2+4y^2-6x+20y-2=0\)

In Exercises 47-50, find the vertex, focus, and directrix of the parabola. Use a graphing utility to graph the parabola. \(x^2 + 4x + 6y -2 = 0\)

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

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. \(x^2-6xy-5y^2+4x-22=0\)