Equation of a Circle
Equation of a Circle
Equation of a Circle
The equation of a circle is given by the formula:
The equation of a circle is given by the formula:
(x − a)² + (y − b)² = R²
where (a , b) is the centre of the circle and R is the radius of the circle.
where (a , b) is the centre of the circle and R is the radius of the circle.
This equation can also be expanded and expressed in this form:
This equation can also be expanded and expressed in this form:
x² + y² + 2fx + 2gy + c = 0
where (−f, −g) is the centre of the circle
where (−f, −g) is the centre of the circle
and √(f ² + g² − c) is the radius of the circle.
and √(f ² + g² − c) is the radius of the circle.
Explore!
Explore!
Use the applet below to explore the relationship between the coordinates of the centre & the radius of the circle with the equation of a circle.
Use the applet below to explore the relationship between the coordinates of the centre & the radius of the circle with the equation of a circle.
Move the centre O and point A (on the circle) to manipulate the circle.
Move the centre O and point A (on the circle) to manipulate the circle.
Test yourself!
Test yourself!
By completing the square or otherwise, can you find the centre and radius of the circle equation given below.
By completing the square or otherwise, can you find the centre and radius of the circle equation given below.
Next: Lets see how the equation of a circle changes under simple transformations.
Next: Lets see how the equation of a circle changes under simple transformations.