a)A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 16 inches across at its opening and is 2 feet deep, where will the light be concentrated? (Round your answer to the nearest tenth.)

b)The letters r and represent polar coordinates. Write the equation using rectangular coordinates (x, y). Write in simplified form.

a.r(1 - 2 cos ) = 1

c)v = 5i + 3j + k, u = 3i + 4j - 3k. Find a vector orthogonal to both v and u.

d)Find z/w . Write the answer in rectangular, exponential, and polar form.

a.z = 3 cos 7 4 + i sin 7 4 , w = 6 cos 9 4 + i sin 9 4

e)Find a so that the vectors v = i + aj and w = -3i + 4j are orthogonal.

f)9x^2 + y^2 - 126x + 432 = 0. Find the center, foci, and vertices of the ellipse. Make sure to write the equation in standard form for an ellipse.

g)Find the direction angles of the vector and write in terms of its magnitude and direction cosines. Round to the nearest degree, if necessary.

a.v = -2i - 3j + 4k

h)Identify, find a table of points, determine symmetry, and use to graph the equation.

a.r = 3 - 4 sin