Question

Write the equation in standard form for the circle passing through (6, 6) centered at the

origin

Answer 1

x² + y² = 72

Explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

The radius is the distance from the centre to a point on the circle.

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 6)

r =
`√((6-0)^2+(6-0)^2)`

=
`√(6^2+6^2)`

=
`√(36+36)`

=
`√(72)`

Thus

x² + y² = (
`√(72)` )² , that is

x² + y² = 72 ← equation of circle