A variable straight line throgh the point of intersction of the two lines x/3+y/2=1 and x/2+y/3=1 meets the co-ordinate axes at A and B .find the locus of the middle point of AB?
2 Answers
Let the equation of the variable straight line which passes through the point of intersection of the two lines
where
Putting
If the variable straight line meets the X- axis at A , then coordinate of A will be
Again putting
If the variable straight line meets the Y- axis at B , then coordinate of B will be
If the mid point of
then
and
Now
So putting
Explanation:
Let
take, the pts.
We are reqd. to determine the Locus of the pt.
In other words, we have to find an Algebraic Eqn. that relates
Clearly,
Naming
Evidently,
Converting
locus as,
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