# Thread: tangent question

1. ## tangent question

The circle $(x+3)^2+(y-4)^2=r^2$ is a tangent to the parabola $y=(x+3)^2+6$
Find the coordinates where the circle is tangent to the parabola.

2. Hello, requal!

A strange problem . . .

The circle $(x+3)^2+(y-4)^2\:=\:r^2$ is a tangent to the parabola $y\:=\:(x+3)^2+6$
Find the coordinates where the circle is tangent to the parabola.
Make a sketch!

The parabola opens upward with vertex (-3,6).
The circle has center (-3,4) and radius $r.$

Since the center of the circle is directly below the vertex of the parabola,
. . the only point at which they can be tangent is at the vertex: . $\begin{array}{c}\cup \\ ^{\bigcirc}\end{array}\!\!\!\leftarrow$