Find an equation of the circle with center at the origin that passes through (4, 5).

Question

Quizplus · Accepted Answer

If a circle has its center at the origin, its equation takes the form:

$x^2 + y^2 = r^2$

where $r$ is the radius of the circle.

Since the circle passes through the point $(4, 5)$, we can substitute these coordinates into the equation:

$4^2 + 5^2 = r^2$

Simplifying:

$r^2 = 41$

Taking the square root of both sides (and noting that $r$ must be positive):

$r = \sqrt{41}$

Thus, the equation of the circle is:

$x^2 + y^2 = 41$

which matches choice (C).

Find an Equation of the Circle with Center at the Origin