Question

How do you find the equation for the circle centered at (0,0) that passes through the point (1,-6)?

Answer 1

`x^2+y^2=37`

Explanation:

The equation of a circle of center(a,b) and radius r is :
`(x-a)^2+(y-b)^2=r^2`

So,to think about the equation of a circle we should think about its center and radius .

The center is given (0,0).
The circle passes through the point (1,-6) so ,
the radius is the distance between (0,0) and (1,-6)

`r^2=(1-0)^2+(-6-0)^2`
`r^2=1+36=37`

Equation of a circle is:

`(x-0)^2+(y-0)^2=37`
`x^2+y^2=37`