# If a circle has center (0,0) and a point on the circle (-2,-4) write the equation of the circle.?

##### 2 Answers

# x^2+ y^2 =20 #

#### Explanation:

The general equation of a circle of radius

# (x-a)^2+ (y-b)^2 =r^2 #

Thus a circle centered on the origin will have an equation of the form:

# x^2+ y^2 =r^2 #

Knowing that

# (-2)^2+ (4)^2 =r^2 #

# :. r^2 = 4 + 16 = 20#

Thus the equation is

# x^2+ y^2 =20 #

#### Explanation:

Every point on a circle has the same distance from the center. This distance is the radius

So, if

To compute the distance between two points

In this case,

Now we know the center

where

which can be rewritten as