x^2+y^2-x-2ky+4=0

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Solution for x^2+y^2-x-2ky+4=0 equation:


Simplifying
x2 + y2 + -1x + -2ky + 4 = 0

Reorder the terms:
4 + -2ky + -1x + x2 + y2 = 0

Solving
4 + -2ky + -1x + x2 + y2 = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -2ky + -1x + x2 + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -2ky + -1x + x2 + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2ky + -1x + x2 + y2 = 0 + -4
-2ky + -1x + x2 + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2ky + -1x + x2 + y2 = -4

Add 'x' to each side of the equation.
-2ky + -1x + x2 + x + y2 = -4 + x

Reorder the terms:
-2ky + -1x + x + x2 + y2 = -4 + x

Combine like terms: -1x + x = 0
-2ky + 0 + x2 + y2 = -4 + x
-2ky + x2 + y2 = -4 + x

Add '-1x2' to each side of the equation.
-2ky + x2 + -1x2 + y2 = -4 + x + -1x2

Combine like terms: x2 + -1x2 = 0
-2ky + 0 + y2 = -4 + x + -1x2
-2ky + y2 = -4 + x + -1x2

Add '-1y2' to each side of the equation.
-2ky + y2 + -1y2 = -4 + x + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
-2ky + 0 = -4 + x + -1x2 + -1y2
-2ky = -4 + x + -1x2 + -1y2

Divide each side by '-2y'.
k = 2y-1 + -0.5xy-1 + 0.5x2y-1 + 0.5y

Simplifying
k = 2y-1 + -0.5xy-1 + 0.5x2y-1 + 0.5y

Reorder the terms:
k = -0.5xy-1 + 0.5x2y-1 + 2y-1 + 0.5y

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