Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane? F. x – y = 1 G. x + y = 25 H. x^2 + y = 25 J. x^2 + y^2 = 5 K. x^2 + y^2 = 25
The distance from the origin to the point (3,4) is the radius of the circle. That distance is √(3² + 4²) = √(9 + 16) = √25 = 5 . The equation of a circle centered at the origin is x² + y² = (radius)² So this circle is [ x² + y² = 25 ] That's Choice-'K'.