Conic Sections Question 233
Question: What is the slope of the tangent line drawn to the hyperbola $ xy=a(a\ne 0) $ at the point (a, 1)
[AMU 2000]
Options:
A) 1/a
B) -1/a
C) a
D) - a
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation of hyperbola $ xy=a $ Slope of tangent at point $ (x_1y_1) $ is $ m={{( \frac{dy}{dx} )} _{(x_1,y_1)}} $ ,
$ \therefore \frac{xdy}{dx}+y=0 $
therefore $ \frac{dy}{dx}=\frac{-y}{x} $ At point $ (a,1); $
$ m={{( \frac{dy}{dx} )} _{(a,1)}}=-\frac{1}{a} $ .
BETA
