Two given straight lines meet in O, and through a given points P is drawn a straight line to meet them in Q and R; if the parallelogram OQSR be completed find the equation of the locus of S

# Two given straight lines meet in O, and through a given points P is drawn a straight line to meet them in Q and R; if the parallelogram OQSR be completed find the equation of the locus of S

1. A
2. B
3. C
4. D

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### Solution:

Let the point S be (x,y) and the fixed point p be (h,k) and the axes be along OQ and OR and coordinates of OQOR are (a,o) and (o,b) respectively.
As the parallelogram OQSR is completed.
It also passes through the point P whose coordinates are (h,k)
Generalizing the equation,
Is the required locus of S.
So, the correct option is 1.

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