Multivariable Calculus - Exam 1

What is the equation for a circle with a center (h,k) and radius r?

What is the equation for a cylinder with radius r?

Equation for an ellipse with center (h,k) and an “a” major-axis and “b” minor-axis

Equation(s) of parabola with vertex (h,k)

Cross product

The what of two vectors produces a vector orthogonal to both of them?

The equation for an ellipsoid

The equation for an elliptical paraboloid pointing ‘up’ in the z-direction

The equation for an elliptical cone pointing ‘up’ and ‘down’ on the z-axis

The equation for a hyperboloid of one sheet pointing ‘up’ and ‘down’ on the z-axis

The equation for a hyperboloid of two sheets pointing ‘up’ and ‘down’ on the z-axis

The equation for a hyperbolic paraboloid with the ‘saddle’ point in the (+z-hat) direction

(After finding a & b)

(after finding magnitude of r-prime)

What is the equation for a horizontal hyperbola with its center at (h,k)?

What is the equation for a vertical hyperbola with its center at (h,k)?