Question

4. Stella says the equation x^2−8x+y^2+2y=5 has a center of (4,−1) and a radius of 5. Is she correct? Why or why not?

Answer 1

Stella is correct about center and wrong about radius      

Step-by-step explanation:

Equation of circle with (h,k) as center and radius r is given by,

          (x-h)²+(y-k)² = r²

Here equation is

          x²−8x+y²+2y=5

Changing in to (x-h)²+(y-k)² = r² form

           x²−8x + 16 - 16 +y²+2y+1 - 1=5  

           (x-4)² - 16 + (y+1)² -1 = 5

           (x-4)²  + (y+1)²  = 22

           (x-4)²  + (y+1)²  = 4.69²

           Center is (4,-1) and radius is 4.69

Stella is correct about center and wrong about radius