91Ó°ÊÓ

In Exercises 19-28, a point in polar coordinates is given. Convert the point to rectangular coordinates. \(\left(0, -\pi\right)\)

In Exercises 19-28, find the standard form of the equation of the ellipse with the given characteristics. Foci: \((0, 0), (4, 0); \quad\) major axis of length \(6\)

In Exercises 19-32, find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: \((-\frac{3}{2}, 0)\)

In Exercises 15-28, identify the conic and sketch its graph. \(r=\dfrac{9}{3-2\cos\ \theta}\)

In Exercises 19-26, find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. \((3, \sqrt{3})\), \((6, -2\sqrt{3})\)

In Exercises 9-22, find the center, vertices, foci, and the equations of the asymptotes of the hyperbola, and sketch its graph using the asymptotes as an aid. \(16y^2-x^2+2x+64y+63=0\)

In Exercises 13-26, rotate the axes to eliminate the \(xy\)-term in the equation. Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. \(13x^2 +6\sqrt{3}xy+7y^2-16 = 0\)

In Exercises 19-28, a point in polar coordinates is given. Convert the point to rectangular coordinates. \(\left(2, 3\pi/4\right)\)

In Exercises 19-32, find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Focus: \((-2, 0)\)

In Exercises 19-26, find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. \((6, 1)\), \((10, 8)\)