Question

Define a circle and derive the equation of the circle whose centre and radius is given. 

Answer 1

Definition: A circle is a set of all points in a plane that are equidistant from a fixed point in a plane. OR A circle is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is constant. 

Note: 

• Fixed point is called centre. 
• The distance from the centre to a point on the circle is called radius. 

Equation of a circle, given its centre and radius: 

Let C(h,k) be the centre y and r, the radius of the circle. 

Let P(x,y) be any point on the circle. Then, by definition, |CPl = r 

∴ By distance formula, we have

Note: If the centre is at the origin ,then h = 0, k = 0. Therefore the equation of the circle with centre at the origin and radius r is x²  + y²  = r²