Assignment:
Q1. a) Find the equation of the sphere that go through the points (1, -3, 4), (1, -5, 2) and (1, -3, 0) and has its center in plane x + y + z = 0.
b) Find the geometric place of the points whose sum of squares of its distances to the planes x+4y+2z=0, 2x –y+z=0 y 2x +y-3z = 0 is equal to 10.
Q2. Study and represent the following ellipsoids
a) 8x^2 + 2y^2 +9z^2 100
b) x^2 + 4y^2 +4z^2-12x =0
Provide complete and step by step solution for the question and show calculations and use formulas.