Question

What is the equation for a circle centered at the origin

Answer 1

A circle can be defined as the locus of all points that satisfy the equation
x2 + y2 = r2
where x,y are the coordinates of each point and r is the radius of the circle.

Hope this helps you.

Answer 2

Answer: The equation of the circle is $x^2+y^2=r^2.$

Step-by-step explanation: We are given to write the equation of a circle centered at the origin.

We know that the standard equation of a circle with center at the point (g, h) and radius 'r' units is given by

$(x-g)^2+(y-h)^2=r^2~~~~~~~~~~~~~~~~~~~~(i)$

The co-ordinates of the origin are (0, 0).

So, if the center of the circle is at the origin, then we have  

(g, h) = (0, 0).

Therefore, from equation (i), we have

$(x-0)^2+(y-0)^2=r^2\\\\\Rightarrow x^2+y^2=r^2.$

Thus, the required equation of the circle is $x^2+y^2=r^2.$