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Grade 12th passAnalytical Geometry

Obtain the locus of the point of intersection of the tangents to the circle x^2+y^2=a^2 which include an angle a

Profile image of Aamina
10 Years agoGrade 12th pass
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1 Answer

Profile image of Vikas TU
ApprovedApproved Tutor Answer10 Years ago
let the tangents eqn. be: and (h,k) be their point of intersection.
y = m1x + c1
y = m2x + c2
a is the angle if then,
a =arctan((m1-m2)/(1 + m1m2))...............(1)
solve both the eqns. of tangents then,
h = (c2 – c1)/(m1 – m2)
k = m2*(c2 – c1)/(m1 – m2) + c2
eliminate m1 m2.

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