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




11 and 12 Grade Math 

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