# 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)$$^{2}$$ = a$$^{2}$$.

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

Then the equation (x - h)$$^{2}$$ + (y - k)$$^{2}$$ = a$$^{2}$$ becomes x$$^{2}$$ + y$$^{2}$$ = a$$^{2}$$

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 x$$^{2}$$ + y$$^{2}$$ = (√5)$$^{2}$$

⇒ x$$^{2}$$ + y$$^{2}$$ = 5

⇒ x$$^{2}$$ + y$$^{2}$$ - 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 x$$^{2}$$ + y$$^{2}$$ = (10)$$^{2}$$

x$$^{2}$$ + y$$^{2}$$ = 100

x$$^{2}$$ + y$$^{2}$$ - 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 x$$^{2}$$ + y$$^{2}$$ = (2√3)$$^{2}$$

x$$^{2}$$ + y$$^{2}$$ = 12

x$$^{2}$$ + y$$^{2}$$ - 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 x$$^{2}$$ + y$$^{2}$$ = (13)$$^{2}$$

x$$^{2}$$ + y$$^{2}$$ = 169

x$$^{2}$$ + y$$^{2}$$ - 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 x$$^{2}$$ + y$$^{2}$$ = (1)$$^{2}$$

x$$^{2}$$ + y$$^{2}$$ = 1

x$$^{2}$$ + y$$^{2}$$ - 1 = 0

The Circle