Question

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

• A. $\sqrt{\frac{r^2(a^2+b^2)-a^2{b}^2}{a^2+b^2}}$
• B. $2\sqrt{\frac{r^2(a^2+b^2)-a^2{b}^2}{a^2+b^2}}$
• C. $2\frac{\sqrt{r^2(a^2+b^2)-a^2{b}^2}}{a^2+b^2}$
• D. $2\frac{\sqrt{r^2(a^2+b^2)+a^2{b}^2}}{a^2+b^2}$

Answer 1

The correct option is B

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

Length of chord

= $2\left\{\right(radius{)}^2-(lengthof\perp fromcentretochord{)}^2{\}}^{1/2}$

= $2\{r^2-⟮\frac{-1}{\sqrt{\left(1/a^2\right)+\left(1/b^2\right)}}{⟯}^2{\}}^{1/2}$

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