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**

**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**__From Centre of the Circle Coincides with the Origin____ to HOME PAGE__

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