In Exercises 71 and 72, show that the tangent plane to the quadric surface at the point

Chapter 13, Problem 72

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In Exercises 71 and 72, show that the tangent plane to the quadric surface at the point can be written in the given form.

\(\text { Hyperboloid: } \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}}=1\)

\(\text { Plane: } \frac{x_{0} x}{a^{2}}+\frac{y_{0} y}{b^{2}}-\frac{z_{0} z}{c^{2}}=1\)

Text Transcription:

Hyperboloid:fracx^2a^2+fracy^2b^2-fracz^2c^2=1

Plane:fracx_0xa^2+fracy_0yb^2-fracz_0zc^2=1

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