Conic Sections Question 56
Question: If $ x=9 $ is the chord of contact of the hyperbola $ x^{2}-y^{2}=9 $ , then the equation of the corresponding pair of tangents is
[IIT 1999]
Options:
A) $ 9x^{2}-8y^{2}+18x-9=0 $
B) $ 9x^{2}-8y^{2}-18x+9=0 $
C) $ 9x^{2}-8y^{2}-18x-9=0 $
D) $ 9x^{2}-8y^{2}+18x+9=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
The equation of chord of contact at point $ (h,k) $ is $ xh-yk=9 $
Comparing with $ x=9, $ we have $ h=1,k=0 $
Hence equation of pair of tangent at point (1,0) is $ SS_1=T^{2} $
therefore $ (x^{2}-y^{2}-9)(1^{2}-0^{2}-9)={{(x-9)}^{2}} $
therefore $ -8x^{2}+8y^{2}+72=x^{2}-18x+81 $
therefore $ 9x^{2}-8y^{2}-18x+9=0 $ .
BETA
