91Ó°ÊÓ

Write an equation of a circle with the given center and radius. Check your answers. $$ (0,0), 10 $$

Write an equation of a circle with the given center and radius. Check your answers. $$ (2,3), 4.5 $$

Write an equation of an ellipse in standard form with center at the origin and with the given vertex and co-vertex. $$ (-6,0),(0,5) $$

Write an equation of a parabola opening upward with a vertex at the origin. focus 1.5 units from vertex

optics A cross section of a flashlight reflector is a parabola. The bulb is located at the focus. Suppose the bulb is located \(\frac{1}{4}\) in. from the vertex of the reflector. Model a cross section of the reflector by writing an equation of a parabola that opens upward and has its vertex at the origin. What is an advantage of this parabolic design?

Identify the conic section represented by each equation by writing the equation in standard form. For a parabola, give the vertex. For a circle, give the center and the radius. For an ellipse or a hyperbola, give the center and the foci. Sketch the graph. \(x^{2}+4 y^{2}-2 x-15=0\)

Find the foci for each equation of an ellipse. Then graph the ellipse. $$ x^{2}+4 y^{2}=16 $$

Write an equation of an ellipse for the given foci and co-vertices. foci \(( \pm 14,0),\) co-vertices \((0, \pm 7)\)

Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) $$ (0,-3) $$

List the properties of a hyperbola that allow you to sketch its graph.