the locus of the point of intersection of the lines x/a cosθ + y/b sinθ=1 and x/asinθ - y/b cosθ =1is
Samuel Sam , 7 Years ago
Grade 12th pass
Analytical Geometry> the locus of the point of intersection of...
1 Answers
Vikas TU
Last Activity: 7 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)
Thapar University)
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