For any two nonzero real numbers a and b,if t | vedclass

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(C) The equation of the circle is $x^2 + y^2 = 1$. The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(x_1, y_1)$ is given by $

Vedclass · Accepted Answer

$\left(\frac{1}{a}, \frac{1}{b}\right)$ lies on the circle

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(C) The equation of the circle is $x^2 + y^2 = 1$. The equation of the tangent to the circle $x^2 + y^2 = r^2$ at the point $(x_1, y_1)$ is given by $x x_1 + y y_1 = r^2$. Here,$r^2 = 1$,so the tangent at $(x_1, y_1)$ is $x x_1 + y y_1 = 1$. We are given that the line $\frac{x}{a} + \frac{y}{b} = 1$ is a tangent to the circle. Comparing this with $x x_1 + y y_1 = 1$,we get $x_1 = \frac{1}{a}$ and $y_1 = \frac{1}{b}$. Since $(x_1, y_1)$ is the point of tangency,it must lie on the circle $x^2 + y^2 = 1$. Therefore,the point $\left(\frac{1}{a}, \frac{1}{b}\right)$ lies on the circle.

For any two nonzero real numbers $a$ and $b$,if the line $\frac{x}{a} + \frac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$,then which of the following is true?

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