Question

What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0

1. minhkhoi
The general form of the equation for the given circle centered at o(0, 0) is x² + y² – 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)²  = r².
• The given equation is x² + y² – 41 = 0 which is also represented by
(x-0)² + (y-0)²  = -(√41)². This is not possible.
• The given equation is x² + y² – 41 = 0 which is also represented by (x-0)² + (y-0)²  = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct
• The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)²  = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect.
• The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)²  = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.
Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² – 41 = 0.