Question
Tangent lines for an ellipse Show that an equation of the line tangent to the ellipse $x^{2} / a^{2}+y^{2} / b^{2}=1$ at the point $\left(x_{0}, y_{0}\right)$ is $$\frac{x x_{0}}{a^{2}}+\frac{y y_{0}}{b^{2}}=1$$.
Step 1
We want to find the equation of the tangent line at the point $(x_{0}, y_{0})$ on the ellipse. Show more…
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Show that an equation of the line tangent to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ at the point $\left(x_{0}, y_{0}\right)$ is $$\frac{x x_{0}}{a^{2}}+\frac{y y_{0}}{b^{2}}=1$$
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Prove: The line tangent to the ellipse $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ at the point $\left(x_{0}, y_{0}\right)$ has the equation $$\frac{x x_{0}}{a^{2}}+\frac{y y_{0}}{b^{2}}=1$$
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Show by implicit differentiation that the tangent line to the ellipse $$ \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 $$ at the point $\left(x_{0}, y_{0}\right)$ has equation $$ \frac{x_{0} x}{a^{2}}+\frac{y_{0} y}{b^{2}}=1 $$
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