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(A) The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(x_1, y_1)$ is given by $xx_1 + yy_1 = r^2$.Here,$x_1 = \frac{ab^2}{a^2

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

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(A) The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(x_1, y_1)$ is given by $xx_1 + yy_1 = r^2$.Here,$x_1 = \frac{ab^2}{a^2 + b^2}$,$y_1 = \frac{a^2b}{a^2 + b^2}$,and $r^2 = \frac{a^2b^2}{a^2 + b^2}$.Substituting these values into the formula:$x \left( \frac{ab^2}{a^2 + b^2} ight) + y \left( \frac{a^2b}{a^2 + b^2} ight) = \frac{a^2b^2}{a^2 + b^2}$Dividing both sides by $\frac{ab}{a^2 + b^2}$ (assuming $a, b 
eq 0$):$xb + ya = ab$Dividing by $ab$:$\frac{xb}{ab} + \frac{ya}{ab} = \frac{ab}{ab}$$\frac{x}{a} + \frac{y}{b} = 1$.

The equation of the tangent at the point $\left( \frac{ab^2}{a^2 + b^2}, \frac{a^2b}{a^2 + b^2} \right)$ to the circle $x^2 + y^2 = \frac{a^2b^2}{a^2 + b^2}$ is

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