Question

Trace the conicoid given by x^2+2z^2=4y What are the sections of this conicoid by the planes x+2=0 and y=1 Describe geometrically.

Answer 1

Answer on Question #46173 - Math - Analytic Geometry

Problem.

Trace the conicoid given by $x^{\wedge}2 + 2z^{\wedge}2 = 4y$ . What are the sections of this conicoid by the planes $x + 2 = 0$ and $y = 1$ ?

Describe geometrically.

Solution.

The intersection of conicoid $x^{2} + 2z^{2} = 4y$ with plane $x + 2 = 0$ is parabola $4 + 2z^{2} = 4y$ (red line) in the plane $x + 2 = 0$ .

The intersection of conicoid $x^{2} + 2z^{2} = 4y$ with plane $y = 1$ is parabola $x^{2} + 2z^{2} = 4$ (blue line) in the plane $y = 1$ .

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