The length of the chord intercepted by the ci | vedclass

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(B) The length of the chord is given by the formula $L = 2\sqrt{R^2 - d^2}$,where $R$ is the radius of the circle and $d$ is the perpendicular distanc

Vedclass · Accepted Answer

$2\sqrt{\frac{r^2(a^2 + b^2) - a^2b^2}{a^2 + b^2}}$

Vedclass · Answer

(B) The length of the chord is given by the formula $L = 2\sqrt{R^2 - d^2}$,where $R$ is the radius of the circle and $d$ is the perpendicular distance from the center $(0, 0)$ to the line $\frac{x}{a} + \frac{y}{b} - 1 = 0$.The radius $R = r$.The perpendicular distance $d = \frac{|\frac{0}{a} + \frac{0}{b} - 1|}{\sqrt{(\frac{1}{a})^2 + (\frac{1}{b})^2}} = \frac{1}{\sqrt{\frac{a^2 + b^2}{a^2b^2}}} = \frac{|ab|}{\sqrt{a^2 + b^2}}$.Substituting these into the formula:$L = 2\sqrt{r^2 - \frac{a^2b^2}{a^2 + b^2}}$$L = 2\sqrt{\frac{r^2(a^2 + b^2) - a^2b^2}{a^2 + b^2}}$.

The length of the chord intercepted by the circle $x^2 + y^2 = r^2$ on the line $\frac{x}{a} + \frac{y}{b} = 1$ is

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