Prove: The line tangent to the ellipsex2a2 + y2b2 = 1at the point (x0, y0) has the

Chapter 10, Problem 52

(choose chapter or problem)

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

$\frac{x x_{0}}{a^{2}}+\frac{y y_{0}}{b^{2}}=1$

Equation Transcription:

$\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$

$({x}_{0},{y}_{0})$

$\frac{x{x}_{0}}{{a}^{2}}+\frac{y{y}_{0}}{{b}^{2}}=1$

Text Transcription:

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

(x_0, y_0)

xx_0 /a^2 +yy_0 /b^2 =1

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