Is this A-Level Maths Question Possible?Watch
The question is not specific to get one answer. There are infinitely many equations describing the diameter, but only one that is parallel to the chord. So perhaps have a go at that - it's possible.
TBH, upon more thinking, not only are there infinitely many diameters, there are also infinitely many circles satisfying the conditions.
So I want to make two important points:
(1) The question is very unclear on what you need to do, and there are many ways to interpret what it wants.
and (2) we can indeed find this special family of circles that satisfy the conditions, and there is a unique equation of the diameter which is common for every single circle. Observe the following animation: https://www.desmos.com/calculator/cifvr1jydf
The task here, which I presume is what the question wants, is to find the equation of the line that the centre of the circle moves along. This line is clearly the diameter to every single circle we can possibly have under the given conditions.