Question

Find the equation of the normal to the curve x^2+y^2+xy=0 at the point (2,2).

Answer 1

5y -x=8

Explanation:

We have given
`x^2+y^2+xy=0`

Differentiating this function with respect to x

`2x+2y+x(dy)/(dx)+y=0`

At point (2,2)

`2* 2+2* 2+2* (dy)/(dx)+2=0`

`(dy)/(dx)= -5`

that is m= -5

The equation of normal is
`](y-y_1)/(x-x_1)=(-1)/(m)[/tex</p><p>[tex](y-2)/(x-2)=(-1)/(-5)`

5y-x=8 this is the equation of normal