MPM 2D1
2.3 EQUATION OF A CIRCLE WITH CENTRE AT THE ORIGIN
What do we know about a circle so far???
If the circle is drawn on the Cartesian Plane and its centre is at the origin or (0, 0), then its general
equation is 𝑥 ! + 𝑦 ! = 𝑟 ! where 𝑟 is the radius of the circle and (𝑥, 𝑦) is any point on the
circumference of the circle.
Illustration:
To graph the circle given its equation is very simple. All you need to do is plot the centre and plot the
x and y intercepts and draw the circle.
EXAMPLE 1:
Given the following equations of circles, state the centre, the radius and the x and y intercepts and graph:
a)
𝑥! + 𝑦! = 9
b) 𝑥 ! + 𝑦 ! = 25
EXAMPLE 2:
Find the equation of the circle given the following information:
a) centre (0, 0) and radius is 4 units
b) centre (0, 0) and x-intercept 10
c) centre (0, 0) and passing through point (3, 4)
d) centre (0, 0) and passing through (-1, 5)
EXAMPLE 3:
Determine algebraically if the point ( -3, 5) lies on the circle, inside the circle or outside the circle defined
by the equation 𝑥 ! + 𝑦 ! = 49. Explain your solution.
EXAMPLE 4:
A stone is dropped into a pond and a ripple effect occurs on the water surface. Assume that the stone
enters the water at the origin and the waves from the ripple effect travel 6cm/min. Find the equation of
the circle after 2 minutes? And then after 45 seconds?