Question

Question #608e5

Answer 1

`y_x=+-sqrt(1-2kx)/k`

Explanation:

`k=1/[x+sqrt(x^2+y^2)]`

`color(white)("XXX")rarr x+sqrt(x^2+y^2)=1/k`

`color(white)("XXX")rarr sqrt(x^2+y^2)=1/k-x`

`color(white)("XXX")rarr x^2+y^2=1/k^2-2x/k+x^2`

`color(white)("XXX")rarr y^2=1/k^2-(2kx)/k^2`

`color(white)("XXX")rarr y=+-sqrt(1-2kx)/k`

Assuming `k` is a (non-zero) constant
and `y` is dependent on the variable `x`
`color(white)("XXX")y_x=+-sqrt(1-2kx)/k`