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A variable line passing through point P(...

A variable line passing through point `P(2,1)` meets the axes at A and B . Find the locus of the circumcenter of triangle `O A B` (where `O` is the origin).

Text Solution

Verified by Experts

The correct Answer is:
`x+2y-2xy=0`
Since triangle OAB is right-angled, its circumcenter is the midpoint of hypotenuse AB.
So, let the midpoint of AB be `Q(h,k)`.
Then the coordinates of A and B are `(2h,0)` and `(0,2h)` respectively. Now, points A,B and P are collinear. Therefore, `|{:(2h,,0,,),(2,,1,,),(0,,2k,,),(2h,,0,,):}|=0`
or `2h+4k-4hk=0`
or `x+2y-2xy=0`
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