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?

A. \( x - y = 1 \)

B. \( x + y = 25 \)

C. \( x^2 + y = 25 \)

D. \( x^2 + y^2 = 5 \)

E. \( x^2 + y^2 = 25 \)

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'.

Answered by AL2006 | 2024-06-10

The equation of the circle centered at (0,0) that passes through the point (3,4) is x 2 + y 2 = 25 . This corresponds to choice E. Thus the correct answer is E.
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Answered by AL2006 | 2024-10-01