91Ó°ÊÓ

Find the vertices and co-vertices of each ellipse. $$ 3 x^{2}+2 y^{2}=6 $$

The foci of a hyperbola are \((0,-4)\) and \((0,8) .\) Which additional information would allow you to write an equation for the hyperbola? F. location of the center G. location of one vertex H. midpoint of transverse axis J. distance from the center to a focus

Suppose \(z\) varies jointly with \(x\) and \(y .\) Write a function that models each relationship. Find the value of \(z\) when \(x=-2\) and \(y=3 .\) \(z=-5\) when \(x=-1\) and \(y=-1\)

Write an equation of an ellipse in standard form with center at the origin and with the given characteristics. focus \((0,-5), y\) -intercept 8

What is the radius of the circle with equation \((x-2)^{2}+3+(y+1)^{2}=7 ?\)

Simplify each expression. \(\ln e\)