Conic Sections Question 171
Question: The point of contact of the line $ y=x-1 $ with $ 3x^{2}-4y^{2}=12 $ is
[BIT Mesra 1996]
Options:
A) (4, 3)
B) (3, 4)
C) (4, -3)
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The equation of the line and hyperbola are $ y=x-1 $ ……(i) $ 3x^{2}-4y^{2}=12 $ ……(ii) From (i) and (ii), we get $ 3x^{2}-4{{(x-1)}^{2}}=12 $
$ \Rightarrow 3x^{2}-4(x^{2}-2x+1)=12 $
or $ x^{2}-8x+16=0 $
therefore $ x=4 $
From (i), $ y=3 $ . So point of contact is $ (4,3) $ .
BETA
