Question

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

Answer 1

x² + y² = 42.25

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`

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`