Plano Tangente

[size=150][justify]Según Claudio Pita Ruíz ( 1995), [i][br]"Si consideramos una función [/i][math]f:U\subseteq\mathbb{R}^2\longrightarrow\mathbb{R}[/math][i] definida en el conjunto abierto [/i][math]U[/math][i] de [/i][math]\mathbb{R}^2[/math][i]. Si suponemos que la función es diferenciable en el punto [/i][math]\left(x_0,y_0\right)[/math][i], queremos asociar a la gráfica de la función un plano tangente, que debe contener todas las rectas tangentes a la superficie en el [/i][math]z=f\left(x,y\right)[/math][i] en el punto [/i][math]\left(x_{0,}y_{0,}f\left(x_0,y_0\right)\right)[/math][i] , [/i][i]lo que buscamos es que si cortamos la superficie con un plano perpendicular, la recta tangente esté contenida en ese plano"[/i][br]La ecuación para poder encontrar el plano tangente es; [br][img]data:image/png;base64,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[/img][br]Para este ejercicio,, como nos solicita el plano tangente paralelo al plano [math]\alpha x+\beta y+\gamma z=\delta[/math], debemos de encontrar los puntos del elipsoide tal que sus vectores normales deben ser también paralelos al plano que nos dan. [br]Es por eso que para calcular los puntos del elipsoide, construimos la función, que es la curva de nivel cero de la expresión, por lo que el gradiente apunta a la dirección normal, después calculamos el gradiente de [math]g=\left(\alpha,\beta,\gamma\right)[/math]. Como [br][math]N^{\longrightarrow1}\mid\mid N^{\longrightarrow2}\Longrightarrow N^{\longrightarrow1}\mid\mid KN^{\longrightarrow2}[/math], Igualamos [math]\left(\frac{x}{a^2,}\frac{y}{b^2},\frac{z}{c^2}\right)=\left(\alpha k,\beta k,\gamma k\right)[/math], el valor de [math]\eta=\sqrt{\alpha^{^2}a^{^2}+\beta^{^2}b^{^2}+\gamma^{^2}c^{^2}}[/math] y al final, tenemos que los puntos del elipsoide son: [math]A=\left(\frac{\alpha a^{^2}}{\eta},\frac{\beta b^{^2}}{\eta},\frac{\gamma c^{^2}}{\eta}\right),B=\left(\frac{-\alpha a^{^2}}{\eta},-\frac{\beta b^{^2}}{\eta},-\frac{\gamma c^{^2}}{\eta}\right)[/math]. Posteriormente, calculamos las ecuaciones del plano tangente, que son: [br][math]\alpha x+\beta y+\gamma z=\eta[/math] y [math]\alpha x+\beta y+\gamma z=-\eta[/math]. [br]Puedes observar en la construcción de GeoGebra, los planos tangentes, los valores del elipsoide e incluso modificar sus dimensiones, así como los valores de [math]\alpha,\beta,\gamma,\delta[/math] con los deslizadores. [/justify][/size]

Information: Plano Tangente