Conic Sections Question 197
Question: Let A be the centre of the circle $ x^{2}+y^{2}-2x-4y-20=0, $ and $ B(1,7) $ and $ D(4,-2) $ are points on the circle then, if tangents be drawn at B and D, which meet at C, then area of quadrilateral ABCD is-
Options:
A) 150
B) 75
C) 75/2
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Here, centre is $ A(1,2) $ , and tangent at $ B(1,7) $ is $ x.1+y.7-1(x+1)-2(y+7)-20=0 $
…… (1) Or $ y=7 $ Tangent at $ D(4,-2) $ is $ 3x-4y-20=0 $
…… (2) Solving (1) and (2), we get C is $ (16,7) $ Area $ ABCD=2(Areaof\Delta ABC)=2\times \frac{1}{2}AB\times BC $
$ =AB\times BC=5\times 15=75 $ units
BETA
