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.

Centre of the Circle Coincides with the Origin

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

• Definition of Circle
• Equation of a Circle
• General Form of the Equation of a Circle
• General Equation of Second Degree Represents a Circle
• Centre of the Circle Coincides with the Origin
• Circle Passes through the Origin
• Circle Touches x-axis
• Circle Touches y-axis
• Circle Touches both x-axis and y-axis
• Centre of the Circle on x-axis
• Centre of the Circle on y-axis
• Circle Passes through the Origin and Centre Lies on x-axis
• Circle Passes through the Origin and Centre Lies on y-axis
• Equation of a Circle when Line Segment Joining Two Given Points is a Diameter
• Equations of Concentric Circles
  
• Circle Passing Through Three Given Points
• Circle Through the Intersection of Two Circles
• Equation of the Common Chord of Two Circles
• Position of a Point with Respect to a Circle
• Intercepts on the Axes made by a Circle
• Circle Formulae
• Problems on Circle

11 and 12 Grade Math 

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