91Ó°ÊÓ

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: \(\quad(2,4) ;\) Directrix: \(\quad x=-4\)

In Exercises \(25-36,\) find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((0,-3),(0,3) ;\) vertices: \((0,-4),(0,4)\)

In Exercises \(25-36,\) find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((-2,0),(2,0) ; y\) -intercepts: \(-3\) and 3

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: \(\quad(-3,4) ;\) Directrix: \(y=2\)

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that \(-\infty< t <\infty.\)) \(x=1+3 \cos t, y=2+3 \sin t ; 0 \leq t<2 \pi\)

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: \((7,-1) ;\) Directrix: \(y=-9\)

In Exercises \(25-36,\) find the standard form of the equation of each ellipse satisfying the given conditions. Foci: \((0,-2),(0,2) ; x\) -intercepts: \(-2\) and 2

Eliminate the parameter t. Then use the rectangular equation to sketch the plane curve represented by the given parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. (If an interval for t is not specified, assume that \(-\infty< t <\infty.\)) \(x=-1+2 \cos t, y=1+2 \sin t ; 0 \leq t<2 \pi\)

Identify each equation without applying a rotation of axes. $$5 x^{2}-2 x y+5 y^{2}-12=0$$

In Exercises \(25-36,\) find the standard form of the equation of each ellipse satisfying the given conditions. Major axis horizontal with length \(8 ;\) length of minor axis \(=4\) center; \((0,0)\)