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Question #608e5

1 Answer

Mar 1, 2017

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

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 $x$
$color(white)("XXX")y_x=+-sqrt(1-2kx)/k$

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