Question
Trace the surface x2/ 4 + y2 /9 - z2/ 4 . Also describe its sections by the planes x = ±2 , algebraically and geometrically.
Answer :
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Skip in 10
The given surface equation is: \[ \frac{x^2}{4} + \frac{y^2}{9} - \frac{z^2}{4} = 0 \] This is a hyperboloid of two sheets. To understand the nature of the surface and describe its sections when \(x = \pm 2\), let's follow the steps: ### Step 1: Solve algebraically for the sections when \(x = 2\) and \(x = -2\) 1. For \(x = 2\): Substitute \(x = 2\) into the equation: \[ \frac{2^2}{4} + \frac{y^2}{9} - \frac{z^2}{4} = 0 \] This simplifies to: \[ 1 + \frac{y^2}{9} - \frac{z^2}{4} = 0 \] Rearranging: \[ \frac{y^2}{9} = \frac{z^2}{4} - 1 \] \[ \frac{y^2}{9} = \frac{4
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