Q. The equation of the circle described on the common chord of the circles x^2+y^2+2x=0 and x^2+y^2+2y=0 as a diameter is
Answers
Answered by
38
circle C1: x² + y² + 2x = 0 : ---- (1)
(x+1)² + y² = 1² center (-1,0) Radius = 1
Circle C2: x² + y² + 2 y = 0 : ---- (2)
x² + (y+1)² = 1² center (0, -1), Radius = 1
Points of Intersection: (1) - (2) => x = y
Substituting it in (1) , we get: x = 0, or -1
So common chord is : AB, where A(0,0) and B(-1, -1)
=> Length of AB : √2
=> Radius of circle with AB as diameter: √2/2 = 1/√2
=> Center of circle: Midpoint of AB: (-1/2, -1/2)
Equation of circle: (x + 1/2)² + (y + 1/2)² = 1/2
x² + y² + x + y = 0
(x+1)² + y² = 1² center (-1,0) Radius = 1
Circle C2: x² + y² + 2 y = 0 : ---- (2)
x² + (y+1)² = 1² center (0, -1), Radius = 1
Points of Intersection: (1) - (2) => x = y
Substituting it in (1) , we get: x = 0, or -1
So common chord is : AB, where A(0,0) and B(-1, -1)
=> Length of AB : √2
=> Radius of circle with AB as diameter: √2/2 = 1/√2
=> Center of circle: Midpoint of AB: (-1/2, -1/2)
Equation of circle: (x + 1/2)² + (y + 1/2)² = 1/2
x² + y² + x + y = 0
kvnmurty:
click on red heart thanks above pls
Similar questions