Is this A-Level Maths Question Possible?

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Baebsae
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Hi Guys,

I was wondering if this question is actually possible Attachment 781232
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3pointonefour
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Baebsae
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(Original post by 3pointonefour)
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ah okay the question is A(2,8) and B(7,4) lie on a circle. The line segment AB is a chord. Find the equation of the diameter
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Baebsae
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(Original post by RDKGames)
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.
are you suggesting that it would be in the form of an inequality or ...
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mnot
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(Original post by Baebsae)
ah okay the question is A(2,8) and B(7,4) lie on a circle. The line segment AB is a chord. Find the equation of the diameter
u cannot calclate the diament but general eqn of circle is r^2 = (x-a)^2 + (y-b)^2. u can make 2 eqns with your coordinates ie 3 unknowns a,b,r (r=0.5d) hence u can determine the relationship of r/d in terms of a & b but not calculate the circles eqn.
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RDKGames
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(Original post by Baebsae)
are you suggesting that it would be in the form of an inequality or ...
No.

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.
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