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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

Sagot :

AL2006idn
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'.
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