Show that the equation of the plane that is tangent to theellipsoid x2a2 + y2b2 +z2c2 =

Chapter 13, Problem 33

(choose chapter or problem)

Show that the equation of the plane that is tangent to the ellipsoid

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

at \(\left(x_{0}, y_{0}, z_{0}\right)\) can be written in the form

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

Equation Transcription:

Text Transcription:

x^2 /a^2 +y^2 /b^2 +z^2 /c^2 =1

(x_0, y_0, z_0)

x_0 x/a^2 +y_0 y/b^2 +z_0 z/c^2 =1

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