Question

Slope of the tangent to a family of curve is given by $\frac{by}{ax}$. What is the slope of the tangent of the orthogonal trajectory of the curve?

• A. $-\frac{ax}{by}$
• B. $\frac{ax}{by}$
• C. $-\frac{by}{ax}$
• D. $\frac{by}{ax}$

Answer 1

The correct option is A $-\frac{ax}{by}$

Let $m_o$ be the slope of the orthogonal trajectory. Then,

$\frac{by}{ax}\times m_o=-1$

$\therefore m_o=-\frac{ax}{by}$