Circle with Centre (0,0) (Leaving Cert Mathematics): Flashcards

Set of all points at a fixed distance from a fixed point (the centre)

The radius (distance from centre to any point on circle)

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

Coordinates of any point on the circle

$2r$ (twice the radius)

$C = 2pi r$

$A = pi r^2$

Substitute coordinates into equation; if equation holds true, point lies on circle

Compare with standard form to identify $r^2$, then take square root: $r = sqrt{r^2}$

Fixed point from which all points on circle are equidistant