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Let C be the circle with centre (0,0) and radius 3 units. the equation of locus of the mid-pts of the chords of the circle that subtend and angleof 120 deg at its center is?

Let C be the circle with centre (0,0) and radius 3 units. the equation of locus of the mid-pts of the chords of the circle that subtend and angleof 120 deg at its center is?

Grade:11

1 Answers

alphaa
13 Points
3 years ago
Consider chord AC join OA and  OC . Draw perpendicular from O TO B( Mid point of  AC). Let coordinates of B be (h,k). The Angle AOC is 120 deg. Thus angle AOB is 60 deg. Therefore,
   Cos 60= OB/OC. 
   1/2= h^2 + K^2/3
By solving and replacing h,k by x,y we get,
x^2 + y2 = 9/4
 
 
    

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