Answer to Question #259265 in Analytic Geometry for Tani

Analytic Geometry

Question #259265

Find the section of the conicoid x^2/2-y^2/3 = 2z by the plane x-2y+z = 1. What conic does this section represent? Justify your answer.

Expert's answer

x-2y+z=1=>z=-x+2y+1

\dfrac{x^2}{2}-\dfrac{y^2}{3} = 2(-x+2y+1)

\dfrac{x^2+4x+4}{2}-\dfrac{y^2+12y+36}{3} =2+2-12

\dfrac{(y+6)^2}{24}-\dfrac{(x+2)^2}{16} =1

The equation represents the hyperbola.

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