Equation of a Circle: Centre at Origin (Grade 12 NSC Matric Mathematics): Flashcards

Set of all points equal distance from a centre

Distance from centre to any point on circumference

Line through centre connecting two points; max distance

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

Pythagorean theorem

If $(x, y)$ on circle, then $(-x, -y)$ also on circle

Substitute coordinates into equation $x^2 + y^2 = r^2$

Diameter = $2 \times$ radius

Infinitely many (any line through centre)

x-axis, y-axis, $y = x$, and $y = -x$