AQA Level 2 Certificate Further Mathematics · 8365

Circle Equation at Origin

What you need to know

Formulate the algebraic equation of a circle centered precisely at the origin when given its radius, utilizing the standard form:

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

2

=

r2

Apply established geometric theorems to solve coordinate geometry problems, identifying that the angle created in a semi-circle is exactly 90 degrees.
Analyze circle properties to mathematically demonstrate that the perpendicular line from the center to a chord perfectly bisects that chord.
Apply the geometric rule stating that the angle formed between a tangent and its corresponding radius is 90 degrees.
Calculate and prove that tangents drawn from a single external coordinate point to a circle are perfectly equal in length.