Circle And System Of Circles Chord Of Contact Of Tangent Pole And Polar Question 7
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 $ is
Options:
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) None of these
Answer:
Correct Answer: B
Solution:
Length of chord $ =2{{{{{(\text{radius)}}^{2}}-{{(\text{length of }\bot \text{from centre to chord})}^{2}}}}^{1/2}} $ $ =2{{{ r^{2}-{{( \frac{-1}{\sqrt{(1/a^{2})+(1/b^{2})}} )}^{2}} }}^{1/2}} $ $ =2\sqrt{\frac{r^{2}(a^{2}+b^{2})-a^{2}b^{2}}{a^{2}+b^{2}}} $ .
BETA
