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the locus of the point of intersection of the lines x/a cos​ θ ​+ y/b sin θ=1 and x/asin θ - y/b cosθ =1 is

the locus of the point of intersection of the lines 
x/a cos​θ ​+ y/b sinθ=1 and x/asinθ - y/b cosθ =1
is
 

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
The two lines given are x/acosθ + y/bsinθ = 1 and  x/asinθ – y/bcosθ = 1.
We can simplify this as
bsinθx + acosθy = absinθcosθ --------- (1)
and 
bcosθx – asinθy = absinθcosθ ----------- (2)
(1) x cosθ – (2) x sinθ => ay =  absinθcosθ(cosθ – sinθ).
Similarly,
(1) x sinθ + (2) x cosθ => bx =  absinθcosθ(cosθ + sinθ).
Therefore the locus of the intersection point is ay/(cosθ – sinθ) = bx/(cosθ + sinθ).
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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