Intersection of two sphere

Fid the constant c such that at any point of intersection of the two shpere

(x - c)^2 + y^2 + z^2 = 3 and x^2 + (y - 1)^2 + z^2 = 1

the corresponding tangent plane will be perpendicular to each other.

Info for you: the the gradient of f is normal to the tangent plane of a level surface f(x) = c.

So if the two gradient vectors are perpendicular, then the planes should be too. I found the two gradient vectors and dot product(ed) them together and set them to 0. But I don't know what the intersection is for (I'm getting an equation of a line for the intersection which doesn't make sense). Any help?