Question

Select the correct answer.

A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O.

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

Answer 1

B is the correct answer

Explanation:

The general form of the equation for a circle centered at the origin (0, 0) is x^2 + y^2 = r^2, where r is the radius of the circle. The radius can be calculated as the distance between the center O (0, 0) and point B (4, 5) on its circumference using the distance formula: r = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((4 - 0)^2 + (5 - 0)^2) = sqrt(16 + 25) = sqrt(41). Therefore, the equation for the given circle centered at O (0, 0) is x^2 + y^2 = 41. The correct answer is B. x^2 + y^2 − 41 = 0.