let P1,P2 be any two points on a circle of radius r centred at the origin O. such that angle(P1OP2) = π/3 , if P is the point of intersection of the tangents to the circle at P1 and P2 ,then the locus of P.
1. 4(x^2+y^2) = 3r^2
2. x^2+y^2 = 3r^2
3. x^2+y^2 = 4r^2
4. 3(x^2+y^2) = 4r^2
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Step-by-step explanation:
first first one is current week of P1 and P2 is equal to each other sites
Answered by
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3(x² + y²) = 4r² is Locus of P
Step-by-step explanation:
∠P1OP2 = π/3 = 60°
=> ∠P1OP = 60/2 = 30°
Cos30° = P1O/OP
=> Cos30° = r / OP
=> OP = r/Cos30°
=> OP = 2r/√3
OP² = (x - 0)² + (y - 0)² ( x & y being coordinates of P)
=> x² + y² = 4r²/3
=> 3(x² + y²) = 4r²
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