Graph x^2+y^2+6x-6y-46=0

Problem

x2+y2+6*x−6*y−46=0

Solution

1. Identify the type of equation by looking at the coefficients of the squared terms. Since the coefficients of x2 and y2 are equal, this is the equation of a circle.

2. Group the x terms and y terms together and move the constant to the other side of the equation.

(x2+6*x)+(y2−6*y)=46

3. Complete the square for the x terms by adding (6/2)2=9 and for the y terms by adding ((−6)/2)2=9 to both sides.

(x2+6*x+9)+(y2−6*y+9)=46+9+9

4. Factor the perfect square trinomials into binomial squares and simplify the constant on the right side.

(x+3)2+(y−3)2=64

5. Determine the center (h,k) and the radius r by comparing the result to the standard form (x−h)2+(y−k)2=r2

h=−3

k=3

r=√(,64)=8

6. Graph the circle by plotting the center at (−3,3) and drawing a circle with a radius of 8 units around it.

Final Answer

(x+3)2+(y−3)2=8

Want more problems? Check here!