Question

Write the equation of the following circle with the marked radius if it is centered at the origin.

Answer 1

Answer:

x² + y² = 42.25

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

here r = 6.5, hence

x² + y² = 6.5², that is

x² + y² = 42.25 ← equation of circle

Answer 2

Answer: $x^2 + y^2 = 42.25$

Step-by-step explanation:

The equation of a circle in center-radius form is:

$(x - h)^2 + (y - k)^2 = r^2$

Where the center is at the point (h, k) and the radius is "r".

Given the circle with radius 6.5 and centered at the origin, you can identify that:

 $h=0\\y=0\\r=6.5$

Then, substituting values into $(x - h)^2 + (y - k)^2 = r^2$, you get:

$(x - 0)^2 + (y - 0)^2 = (6.25)^2$

$x^2 + y^2 = 42.25$