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if A(-5,0),B(5,0) and P moves such that PA/PB=2/1 and mximum area of trianglePAB=100/3 sq. units then locus of the point P is a circle No. of such triangles PAB are 2 No. of such triangles PAB are 4 locus of the point is a parabola

if A(-5,0),B(5,0) and P moves such that PA/PB=2/1 and mximum area of trianglePAB=100/3 sq. units then 
  1. locus of the point P is a circle  
  2. No. of such triangles PAB are 2
  3. No. of such triangles PAB are 4
  4. locus of the point is a parabola

Grade:12

1 Answers

Aditya Gupta
2080 Points
2 years ago
let coordinates of P be (x,y).
given that PA= 2PB
or PA^2= 4PB^2. now use distance formula
(x+5)^2 + y^2= 4[(x – 5)^2 + y^2]
or 50x= 3(x^2+y^2) + 75
or (x – 25/3)^2 + (y – 0)^2= (20/3)^2, which obviously represents a circle.
now by drawing diagram, you can see that there are 2 such triangles.
kindly apprrove ;)

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