Find the Domain x^2+y^2-20y+100=y^2-12y+36

Problem

x2+y2−20*y+100=y2−12*y+36

Solution

1. Simplify the equation by subtracting y2 from both sides.

x2−20*y+100=−12*y+36

2. Isolate the y terms by adding 20*y to both sides and subtracting 36 from both sides.

x2+64=8*y

3. Solve for y by dividing the entire equation by 8 to express the relation as a function of x

y=(x2+64)/8

y=1/8*x2+8

4. Identify the domain by observing that the resulting equation is a quadratic function. Since there are no denominators containing x no square roots of negative values, and no logarithms, the function is defined for all real numbers.

Domain=(−∞,∞)

Final Answer

Domain of *x2+y2−20*y+100=y2−12*y+36* is *(−∞,∞)

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