Answer:
C
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius )
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (3, 6)
r = ![\sqrt{(3-0)^2+(6-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%283-0%29%5E2%2B%286-0%29%5E2%7D)
= ![\sqrt{3^2+6^2}](https://tex.z-dn.net/?f=%5Csqrt%7B3%5E2%2B6%5E2%7D)
= ![\sqrt{9+36}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B36%7D)
=
⇒ r² = (
)² = 45, thus
x² + y² = 45 → C