Question

The family of curves represented by $\frac{d{y}_1}{dx}=\frac{x^2+x+1}{y^2+y+1}$ and the family represented by $\frac{d{y}_2}{dx}+\frac{y^2+y+1}{x^2+x+1}=0$

• A. touch each other
• B. orthogonal to each other
• C. identical
• D. intersect at an angle of $\frac{\pi }{4}$

Answer 1

The correct option is B orthogonal to each other

$\left(\frac{d{y}_1}{dx}\right)\times \left(\frac{d{y}_2}{dx}\right)=\left(\frac{x^2+x+1}{y^2+y+1}\right)\left(\frac{-(y^2+y+1)}{(x^2+x+1)}\right)$$=-1$
$Theyareorthogonaltoeachother$