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. x2 + y2 − 41 = 0

Step-by-step explanation:

The correct answer is: B. x2 + y2 − 41 = 0

The general form of the equation of a circle centered at (0, 0) is: x^2 + y^2 = r^2, where r is the radius of the circle.

In this case, the circle is centered at (0, 0), and point B (4, 5) lies on the circumference of the circle. Therefore, the distance between the center of the circle and point B is the radius of the circle. This distance can be calculated using the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for x1, y1, x2, and y2, we get:

distance = √((4 - 0)^2 + (5 - 0)^2)

distance = √(4^2 + 5^2)

distance = √41

Therefore, the radius of the circle is √41, and the equation of the circle is:

x^2 + y^2 = (√41)^2

x^2 + y^2 = 41

Thus, the correct answer is B. x^2 + y^2 − 41 = 0.