2. (a) Find the equation of the sphere which touches the sphere $x^2 + y^2 + z^2 + 2x + 6y + 1 = 0$ at the point $(1, 2, -2)$ and passes through the origin. 7 (b) Find the equation of the cone whose vertex is at the point $(1, 1, 3)$ and which passes through the ellipse $4x^2 + z^2 = 1$, $y = 4$. 7
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