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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.
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
- 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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