Given that y^2=-x^2+4, what is the radius of the circle?

Answer 1

Given: y² = -x² + 4 What is the radius of the circle?

Simple Solution: Just rearrange the given equation to x² + y² = r²

x² + y² = 4 ==> r² = 4

r = 2 (ignore negative root)

Answer 2

Equation of Circle: (Cartesian coordinates)

 for a circle with center (j, k) and radius (r):

  (x-j)^{^2} + (y-k)^{^2} = r^{^2}

 The given equation is:

 y^{^2} = - x^{^2} + 4

  x^{^2} + y^{^2} = 4

  (x-0)^{^2} + (y-0)^{^2} = 2^{^2} [ Center (j,k) is (0,0); radius, r=2 ]