Identify the center and radius of the circle with the given equation in each item.

Question

x²+y²-5x+4y=46

Answer 1

x² - 5x + y² + 4y = 46

x² - 5x + (5/2)² + y² + 4y + 2² = 46 + 25/4 + 4    Completion of square

(x - 5/2)² + (y + 2)² = 225/4

 

 

What is the center and the radius?

Answer 2

 

x^2 - 5x     +  y^2 + 4y   = 46   <---- groups like variables

 

x^2 - 5x + 25/4   + y^2 + 4y + 4 = 46 + 25/4 + 4 <--- completes the square

 

(x - 5/2)^2 + (y+2)^2 = 50 + 25/4  = 225/4

 

The center is (5/2,-2)

the radius is 15/2