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Given the equation of the parabola Find the vertex: [v] Find the focus: [f]

Given the ellipse

Write an explicit formula for the sequence:

Write the equation of the hyperbola illustrated in the graph above.

An arch has the shape of a semi-ellipse. The arch has a height of [b] feet and a span of [a] feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is [y] feet. Round to the nearest hundredth.

Write the following sum using sigma notation:

Determine the equation in standard form of the ellipse illustrated in the graph above.  

Given the equation of the hyperbola

The sides of a nuclear power plant cooling tower form a hyperbola.  The diameter of the bottom of the tower is [bottom] feet.  The smallest diameter of the tower is [center] feet which is [hc] feet above the ground.  The tower is [height] feet tall. Find the width of the tower at a height of [h] feet. Round to the nearest integer.

Find the first term and common difference of the arithmetic sequence whose term is