What is the general form of the equation for the given circle centered at O(0, 0)?
Solution:
The standard form of the equation of a circle with center O (a, b) and radius r is
(x - a)2 + (y - b)2 = r2
It is given that
(a, b) = (0, 0)
r = BO
r2 = BO2
r2 = (4 - 0)2 + (5 - 0)2
r2 = 16 + 25
r2 = 41
The equation of a circle which satisfies the given condition center at the origin and passing through B (4, 5) is
x2 + y2 = 41
x2 + y2 - 41 = 0
Therefore, the general form of the equation of a circle is x2 + y2 - 41 = 0.
What is the general form of the equation for the given circle centered at O(0, 0)?
Summary:
The general form of the equation for the given circle centered at O(0, 0) is x2 + y2 - 41 = 0.