Question

If at any point on a curve the sub-tangent and sub-normal are equal, then length of tangent is

• A. $\sqrt{2|y|}$
• B. $\sqrt{2}$|y|
• C. |y|
• D. None of these

Answer 1

Answer: (B)

$\sqrt{2}$|y|

Answer 2

$\left| y\frac{dy}{dx} \right|$ = $\left| \frac{y}{dy/dx} \right|$

Ž $\left| \frac{dy}{dx} \right|^{2}$ = 1 Ž $\left| \frac{dy}{dx} \right|$ = 1

length of tangent = $\left| \frac{y\sqrt{1 + (dy/dx)^{2}}}{dy/dx} \right|$ = $\left| \frac{y\sqrt{1 + 1}}{1} \right|$

= |y|$\sqrt{2}$