Question

What is the equation of a circle centered at the origin with radius 20.. i cant find the answer and i even tried?

Answer 1

Answer:

Required equation of circle is x² + y² = 400

Step-by-step explanation:

We are given center of the circle i origin and radius = 20 units.

We have to find the equation of the circle.

We know that coordinates of the origin is ( 0 , 0 )

To write the equation of circle we use standard equation of circle,

Standard equation of circle is given as below,

( x - h )² + ( y - k )² = r²

here, ( h , k ) is coordinate of the center of the circle. and r is radius of the circle.

Using given information and standard equation of circle, we have

( x - 0 )² + ( y - 0 )² = 20²

x² + y² = 400

Therefore, Required equation of circle is x² + y² = 400

Answer 2

General equation of a circle with centre (h, k) is given by:

$(x - h)^{2} + (y - k)^{2} = r^{2}$

Now, the origin is the centre and radius is 20, so substituting these points in yields:
$x^{2} + y^{2} = 20^{2}$
$x^{2} + y^{2} = 400$