Question #608e5

1 Answer
Alan P.
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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