Let PQ and MN be two straight lines touching the circle x^2+y^2-4x-6y-3=0 at the points A and B respectively. Let O be the centre of the circle and ∠ AOB= /3. Then the locus of the point of intersect…

Question

Let PQ and MN be two straight lines touching the circle x^2+y^2-4x-6y-3=0 at the points A and B respectively. Let O be the centre of the circle and ∠ AOB= /3. Then the locus of the point of intersection of the lines PQ and MN is :

Accepted Answer

Correct answer: C. (c) Circle: (x-2 )^2+ (y-3 )^2=16, center O= (2 ,3 ), radius r=4. For tangents from external point P touching at A and B with ∠ AOB= /3 : In quadrilateral OAPB : ∠ APB= - /3=2 /3, so ∠ OPA= /3. In right triangle OAP : sin ⁡ ( /3 )= 4 OP. OP= 8 3= 8 33. Locus: (x-2 )^2+ (y-3 )^2= 643. 3(x^2+y^2)-12x-18y-25=0.

$Let PQ and MN be two straight lines touching the circle x^{2} + y^{2} - 4 x - 6 y - 3 = 0 at the points A and B respectively. Let O be the centre of the circle and ∠ AOB = π /3 . Then the locus of the point of intersection of the lines PQ and MN is :$

Solution

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