Question

Sub-normal to $xy=54$ at any point on it varies directly as

• A. cube of ordinate
• B. square of ordinate
• C. ordinate
• D. cube of abscissa

Answer 1

The correct option is A cube of ordinate

$SN=|ym|$

$m=\frac{dy}{dx}=\frac{-54}{x^2}$

$SN=|\frac{-y.54}{x^2}|$

$SN=|\frac{-y.54}{\frac{(54{)}^2}{y^2}}|$

$SN=|\frac{y^3}{54}|$

$SN\alpha y^3$

$SN\alpha \frac{1}{x^3}$