Q: I was always taught that if you engage your gluteal muscles in a leg extension, you can take the workload off the quads. Is that true?
A: The short answer is no—not if it's a front or side extension. In order to lift the leg to the front or side, many muscles need to contract, including the quads, the deeper hip flexor (iliopsoas) and the external rotators found deep within the hip. During the extension to the side, the lateral hip muscles must actively engage. Perhaps the myth began because dancers felt fatigue in various muscles during développé, including the rotators, which are underneath the bigger gluteal muscles, and mistakenly assumed they were actually engaging their glutes.
In arabesque, the glutes contract to take the leg back, while the quads lengthen to allow it. If a dancer tries to engage both the front and the back of the hip at the same time (meaning contract both the quads and the glutes), it is like the two muscles are at war in the joint, and movement becomes strained.
Instead of thinking of muscle engagement, try using imagery, such as becoming a star with light shining through arms, legs and head, to keep equal energy throughout the body. That way the whole body is supporting the extension rather than focusing on just the height of the working leg.