What is the center and radius of the circle whose equation is ?

Question

Xsquared+7X+Ysquared-6Y-7=0

Answer 1

There is also another way!!!!!!

x² + y² + 7x -6y -7 =0

The general equation of a circle is

x²+ y² + 2gx + 2fy +c = 0

comparing these two equations we get

g = 7/2

f  = -6/2 =-3

c = -7

Center = ( -g , -f )

center = (-7/2 , -3 )

Radius =√g² + f ² -c

           = √49/4 + 9 - (-7)

            = √(49 +36 + 28)/4

            = √ (113/4)

            = √113 / 2

Answer 2

x² + 7x + y² - 6y - 7 = 0

complete the squares

x²+7x + (3.5)² + y²-6y + (-3)² = 7+ (3.5)² + (-3)²

(x+3.5)² + (y-3)² = 28.25

center at (-3.5, 3)

radius = √28.25 = 5.3

Answer 3

x^2 + 7x + y^2 - 6y = 7

Complete the square for x and y:

x^2 + 7x + 49/4 + y^2 - 6y + 9 = 7 + 49/4 + 9

(x+7/2)^2 + (y-3)^2 = 113/4

Center is (-7/2, 3)

Radius is sqrt(113)/2

Answer 4

(x^2 + 7x + 49/4) + ( y^2 - 6y + 9 ) = 7 + 49/4 + 9

(x + 3.5) ^2 + (y - 3) ^2 = 28.25

Center is ( -3.5, 3)

Radius is sqr(28.25)

Good luck to you !  

Answer 5

(x+7/2)^2 - (7/2)^2 + (y-3)^2 - 3^2 - 7 = 0

(x+7/2)^2 + (y-3)^2 = 113/4

centre: (-7/2, 3)

radius: sqrt(113)/2