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A and B arre two variable points on the circle x 2 +y 2 -4x-4y-4 √3-2=0 whose centre is at C.if the area of larger sector CAB is eleventimes the area of smaller sector CAB. the locus of point of intersection of tangents at A and B is a circle then its radius is?????????

A and B arre two variable points on the circle x2+y2-4x-4y-4√3-2=0
whose centre is at C.if the area of larger sector CAB is eleventimes the area of smaller sector CAB. the locus of point of intersection of tangents at A and B is a circle then its radius is?????????
 

Grade:11

1 Answers

Vikas TU
14149 Points
2 years ago
Let the points on ellipse be p(acos(θ),bsin(θ)) and
Q(acos(π/2+θ),bsin(π/2+θ))=(−asinθ,bcosθ)
Equation of tangent at point p:
x/acosθ+y/bsinθ=1
Equation of tangent at point Q:
−x/asinθ+y/bcosθ=1
On solving these equations we get, x/a=(cosθ−sinθ)
y/b=(cosθ+sinθ)
On squaring and adding these equations,
2=(x/a)^2+(y/b)^2 Therefore,
(x/a√2)^2+(y/b√2)^2=1

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