#### Problem 44E

44. Show by implicit differentiation that the 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

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