Conic Sections Question 204
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
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:
[b] The equation of tangent at a point $ (x_1,y_1) $ on the hyperbola $ x^{2}-y^{2}=c $ is given by $ xx_1-yy_1=c $ Chord $ x=9 $ meets $ x^{2}-y^{2}=9 $ at $ (9,6\sqrt{2}) $ and $ (9,-6\sqrt{2}) $ at which tangents are $ 9x-6\sqrt{2}y=9 $ and $ 9x+6\sqrt{2}y=9 $ or $ 3x-2\sqrt{2}y-3=0 $ and $ 3x+2\sqrt{2}y-3=0 $
$ \therefore $ Combined equation of tangents is $ (3x-2\sqrt{2}y-3)(3x+2\sqrt{2}y-3)=0 $ or $ 9x^{2}-8y^{2}-18x+9=0 $
BETA
