Equation of a Circle
Equation of a Circle Notes
We find the equation of a circle from the coordinates of its centre and its radius. Consider this circle whose centre is at the point (a,b) and whose radius is r. The equation of the circle is given by
The values of $a$, $b$ and $r$ are specified whereas $x$ and $y$ are left as general points. This is much like when we specify $m$ and $c$ in $y=mx+c$ when we have the equation of a given straight line. Note that the equation of a straight line is explicit – y is the subject and is given in terms of x. The circle equation, on the other hand, is implicit – the $x$s and $y$s are mixed up.
Things to Learn for Circle Equation Questions
You should know the following facts:
- Most importantly, the equation of a circle.
- Secondly, that the angle subtended from a diameter at the circumference is a right angle.
- Next, the radius and tangent touch at right angles to one another.
- Finally, a perpendicular from a chord bisects the chord.
You should be able to find the equation of a circle:
- using completing the square and/or Pythagoras,
- given a triangle that has all three points on its circumference and
- find the equation of a tangent using perpendicular gradients.