Question

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$ If the curve passes through the point $(1,2)$ and $(8,1)$, then $\left|y\left(\frac{1}{8}\right)\right|$ is equal to

• A. $2 \log _{ e } 2$
• B. 4
• C. 1
• D. $4 \log _{ e } 2$

Answer 1

Answer: (B)

4

Answer 2

dxdy​=−xαy​
ydy​=−xα​dx
⇒ydy​+xα​dx=0
⇒ℓny+αℓnx=ℓnc
⇒yxα=c
For (1,2)⇒2.1α=c⇒c=2
For (8,1)⇒1.8α=2⇒α=31​
∴ curve is y=2x−1/3
At x=1/8,y(1/8)=2(81​)−31​⇒y=4