Find the curve for which the length of normal is equal to the radius vector.

Answer

`y^(2)+-x^(2)=c`

Explanation

Length of normal `=ysqrt(1+((dy)/(dx))^(2))` and radius vector `=sqrt(x^(2)+y^(2))`
`therefore y^(2)[1+((dy)/(dx))^(2)]=x^(2)+y^(2)`
or `y(dy)/(dx) =+-x`
or `ydy+-xdx=0` or `y^(2)+-x^(2)=c`