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To prove the locus of a variable line. We have given two diffrent line and we have to prove the locus of the point a new point from by the line joinings

To prove the locus of a variable line.
We have given two diffrent line and we have to prove the locus of the point a new point from by the line joinings

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Grade:11

1 Answers

Aditya Gupta
2081 Points
4 years ago
coordinates: A(a, 0); B(0, b); C(c, 0) and D(0, d)
now, eqn of line AD: dx + ay= ad
similarly BC: bx + cy= bc
let them intersect at (h, k). by solving the eqns simultaneously we obtain 
h= (cab – cad)/(ab – cd) and
k= (bda – bdc)/(ab – cd)
adding
h+k= (ba(c+d) – cd(a+b))/(ab – cd) 
given a+b= c+d
so h+k= (ba(a+b) – cd(a+b))/(ab – cd)= (a+b)(ab – cd)/(ab – cd)= a+b
repace h and k by x and y. so that
x + y= a + b
kindly approve :))
 

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