Determine the equation of a circle that is centered at (0,0) and passes through the point (1,-5).

The equation of the circle that is centered at (0,0) and passes through the point (1,-5) is x 2 + y 2 = 26 . This is derived from the standard equation of a circle using the distance formula to determine the radius. The radius is calculated as 26 ​ .
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Answered by Anonymous | 2025-07-04

To determine the equation of a circle that is centered at the origin (0,0) and passes through the point (1,-5), we can use the standard form equation of a circle centered at the origin:
x 2 + y 2 = r 2
where r is the radius of the circle.
Since the circle passes through the point (1, -5), we can substitute these coordinates into the equation to find the value of r .
Substituting x = 1 and y = − 5 :
1 2 + ( − 5 ) 2 = r 2
Calculating, we get:
1 + 25 = r 2
r 2 = 26
Thus, the equation of the circle is:
x 2 + y 2 = 26
This equation represents a circle with its center at the origin and a radius equal to 26 ​ .

Answered by AvaCharlotteMiller | 2025-07-06