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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

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
 

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 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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