Conic Sections Question 97
Question: The equation of the tangents to the hyperbola $ 3x^{2}-4y^{2}=12 $ which cuts equal intercepts from the axes, are
Options:
A) $ y+x=\pm 1 $
B) $ y-x=\pm 1 $
C) $ 3x+4y=\pm 1 $
D) $ 3x-4y=\pm 1 $
Show Answer
Answer:
Correct Answer: B
Solution:
The tangent at $ (h,k) $ is $ \frac{x}{4/h}-\frac{y}{3/k}=1 $
$ \therefore \frac{4}{h}=\frac{3}{k} $
therefore $ \frac{h}{k}=\frac{4}{3} $ ……(i) and $ 3h^{2}-4k^{2}=12 $ …..(ii) As point $ (h,k) $ lies on it, using (i) and (ii), we get the tangent as $ y-x=\pm 1 $ .
BETA
