91Ó°ÊÓ

In Exercises 35-46, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: \((1, 2), (1, -2); \quad\) passes through the point: \((0, \sqrt{5})\)

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(3, 0\right)\)

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

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

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. \(9x^2+4y^2-54x+40y+37=0\)

In Exercises 37-46, find the angle \(\theta\) (in radians and degrees)between the lines. \(x + 2y = 8\) \(x - 2y = 2\)

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

In Exercises 23-48, sketch the graph of the polar equation using symmetry, zeros, maximum \(r\)-values, and any other additional points. \(r= 2\ \sec\ \theta\)

In Exercises 33-46, find the vertex, focus, and directrix of the parabola, and sketch its graph. \(y=\frac{1}{4}(x^2 - 2x + 5)\)

In Exercises 35-46, find the standard form of the equation of the hyperbola with the given characteristics. Vertices: \((1, 2), (3, 2); \quad\) asymptotes: \(y=x, y=4-x\)