Question

Question #09598

Answer 1

There are three common tangents.

Explanation:

Generally speaking, equation
`(x-a)^2+(y-b)^2=R^2`
describes a circle of the radius `R` with a center at point `O(a,b)`.

The first equation can be transformed into
`x^2+(y-1/2)^2=(1/2)^2`
This equation describes a circle of a radius `1/2` with a center at point `(0,1/2)`.

The second equation can be transformed into
`x^2+(y+1/2)^2=(1/2)^2`
This equation describes a circle of a radius `1/2` with a center at point `(0,-1/2)`.

Obviously, these two circles are tangential to each other with a common point at `(0,0)`.