Conic Sections Question 257
Question: The equation of the hyperbola whose directrix is $ 2x+y=1 $ , focus (1, 1) and eccentricity $ =\sqrt{3} $ , is
Options:
A) $ 7x^{2}+12xy-2y^{2}-2x+4y-7=0 $
B) $ 11x^{2}+12xy+2y^{2}-10x-4y+1=0 $
C) $ 11x^{2}+12xy+2y^{2}-14x-14y+1=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ S(1,1) $ , directrix is $ 2x+y=1 $ and $ e=\sqrt{3} $ . Now let the various point be $ (h,k) $ , then accordingly $ \frac{\sqrt{{{(h-1)}^{2}}+{{(k-1)}^{2}}}}{\frac{2h+k-1}{\sqrt{5}}}=\sqrt{3} $ Squaring both the sides, we get $ 5[{{(h-1)}^{2}}+{{(k-1)}^{2}}]=3{{(2h+k-1)}^{2}} $ On simplification, the required locus is $ 7x^{2}+12xy-2y^{2}-2x+4y-7=0 $ .
BETA
