The family of curves represented by `(dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1)` and the family represented by `(dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0`

Options

A. Touch each other
B. Are orthogonal
C. Are one and the same
D. None of these

Answer

B

Explanation

For the family of curves represented by the first differential equation, the slope of the tangent at any point (x,y) is given by
`((dy)/(dx))_(c_(1))=(x^(2)+x+1)/(y^(2)+y+1)`
For the family of curves represented by the second differential equation, the slope of the tangent at any point is given by
`((dy)/(dx))_(c_(2))=-(y^(2)+y+1)/(x^(2)+x+1)`
Clearly, `((dy)/(dx))_(C_(1)) xx ((dy)/(dx))_(c_(2)) = -1`