Applications Of Derivatives Question 152
Question: If the normal to the curve $ y^{2}=5x-1 $ , at the point (1, -2) is of the form $ ax-5y+b=0 $ , then a and b are
[Pb. CET 2001]
Options:
A) 4, - 14
B) 4, 14
C) -4, 14
D) -4, -14
Show Answer
Answer:
Correct Answer: A
Solution:
We have, $ y^{2}=5x-1 $ …………..(i)
At $ (1,-2) $ ; $ \frac{dy}{dx}={{[ \frac{5}{2y} ]} _{(1,,-2)}}=\frac{-5}{4} $
$ \therefore $ Equation of normal at the point (1, -2) is, $ [y-(-2)],[ \frac{-5}{4} ]+x-1=0 $
$ \therefore 4x-5y-14=0 $ –(ii)
As the normal is of the form $ ax-5y+b=0 $ , comparing this with (ii), we get
$ a=4 $ and $ b=-14 $ .
BETA
