Find the Domain x^2+y^2-2x+4x-6361=0

Problem

x2+y2−2*x+4*y−6361=0

Solution

1. Identify the type of equation. This is a quadratic equation in two variables, x and y representing a circle in the Cartesian plane.

2. Group the x terms and y terms together to prepare for completing the square.

x2−2*x+y2+4*y=6361

3. Complete the square for the x terms by adding ((−2)/2)2=1 to both sides.

(x2−2*x+1)+y2+4*y=6361+1

4. Complete the square for the y terms by adding (4/2)2=4 to both sides.

(x−1)2+(y2+4*y+4)=6362+4

5. Simplify the equation into the standard form of a circle (x−h)2+(y−k)2=r2

(x−1)2+(y+2)2=6366

6. Determine the radius r from the constant on the right side.

r=√(,6366)

7. Find the domain by considering the horizontal extent of the circle. The domain of a circle centered at (h,k) with radius r is the interval [h−r,h+r]

h−r=1−√(,6366)

h+r=1+√(,6366)

Final Answer

Domain=[1−√(,6366),1+√(,6366)]

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