To move anchors or tangents on a Bezier curve
With an anchor selected you can press the Up and Down Arrow keys to select an anchor’s tangent points as well as adjacent anchors.
You can use the Bezier Curve Tool to move tangents while maintaining the current tangent angle (the angle between the two tangents).
To move tangents while maintaining tangent angles
The tangent moves but only in the direction that preserves the tangent angle.
To scale tangents on a Bezier curve