Circle And System Of Circles Question 2
Question: If OA and OB be the tangents to the circle $ x^{2}+y^{2}-6x-8y+21=0 $ drawn from the origin O, then AB =
Options:
A) 11
B) $ \frac{4}{5}\sqrt{21} $
C) $ \sqrt{\frac{17}{3}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Here the equation of AB (chord of contact) is $ 0+0-3(x+0)-4(y+0)+21=0 $
$ \Rightarrow 3x+4y-21=0 $ …………. (i) CM = perpendicular distance from (3, 4) to line (i) is $ \frac{3\times 3+4\times 4-21}{\sqrt{9+16}}=\frac{4}{5} $
$ AM=\sqrt{AC^{2}-CM^{2}}=\sqrt{4-\frac{16}{25}}=\frac{2}{5}\sqrt{21} $
$ \therefore \ \ AB=2AM=\frac{4}{5}\sqrt{21} $ .
BETA
