The equation of the locus of the mid- points of the chords of the circle x2 + y2 = 9 - Maths - Conic Sections

Question

The equ​ation of the locus of the mid- points of the
chords of the circle x2 + y2​ = 9 which
subtend an angle of 2 pi/3 at its centre is = ?

Rahul Raj · Accepted Answer

Dear student

x2+y2=9centre is (0,0) and radius = 3let the midpoint of the chord be (h,k)the chord subtends angle of 2π/3  i
e 120 at centreangle made by the radius at each end of the chord =(180-120)/2=30sin30=distance of midpoint of chord from centreraius of circle12=(h-0)2+(k-0)2332=(h)2+(k)2(h)2+(k)2=9/4locus is x2+y2=9/4circle with the same centre and radius equal to half of it

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The equ​ation of the locus of the mid- points of the chords of the circle x2 + y2​ = 9 which subtend an angle of 2 pi/3 at its centre is = ?

The equation of the locus of the mid- points of the chords of the circle x² + y² = 9 which subtend an angle of 2 pi/3 at its centre is = ?