Mathematical Methods Assignment
Q1. Show that the equation represents an ellipsoid and find its centre
3x2 + 2y2 + 6z2 - 6x + 4y - 24z + 23 = 0.
Q2. Find an equation of the plane through the points P1(1, 1, 1) and P2(2, 0, 1) and perpendicular to the plane x + y + z = 3.
Q3. Write down the following equation in spherical and cylindrical coordinates. Identify the surface given by that equation.
x2 + y2 - z2 = 1.
Q4. Find the length of the curve r→(t) = (et, e-t, √2 t,), -1 ≤ t ≤ 1.
Q5. Find the partial derivatives of the functions
(a) f(x, y) = xyln(x) + xey,
(b) f(x, y) = xsin(y) + yx.