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Centre of the Circle Coincides with the Origin

We will learn how to form the equation of a circle when the centre of the circle coincides with the origin.

The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)2 + (y - k)2 = a2.

When the centre of the circle coincides with the origin i.e., h = k = 0.

Centre of the Circle Coincides with the OriginCentre of the Circle Coincides with the Origin

Then the equation (x - h)2 + (y - k)2 = a2 becomes x2 + y2 = a2

Solved examples on the central form of the equation of a circle whose centre coincides with the origin:

1. Find the equation of the circle whose centre coincides with the origin and radius is √5 units.

Solution:

The equation of the circle whose centre coincides with the origin and radius is √5 units is x2 + y2 = (√5)2

⇒ x2 + y2 = 5

⇒ x2 + y2 - 5 = 0.


2. Find the equation of the circle whose centre coincides with the origin and radius is 10 units.

Solution:

The equation of the circle whose centre coincides with the origin and radius is 10 units is x2 + y2 = (10)2

⇒ x2 + y2 = 100

⇒ x2 + y2 - 100 = 0.

 

3. Find the equation of the circle whose centre coincides with the origin and radius is 2√3 units.

Solution:

The equation of the circle whose centre coincides with the origin and radius is 2√3 units is x2 + y2 = (2√3)2

⇒ x2 + y2 = 12

⇒ x2 + y2 - 12 = 0.


4. Find the equation of the circle whose centre coincides with the origin and radius is 13 units.

Solution:

The equation of the circle whose centre coincides with the origin and radius is 13 units is x2 + y2 = (13)2

⇒ x2 + y2 = 169

⇒ x2 + y2 - 169 = 0


5. Find the equation of the circle whose centre coincides with the origin and radius is 1 unit.

Solution:

The equation of the circle whose centre coincides with the origin and radius is 1 unit is x2 + y2 = (1)2

⇒ x2 + y2 = 1

⇒ x2 + y2 - 1 = 0

● The Circle




11 and 12 Grade Math 

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