the locus of mid points of the chords of the ellipse 2x^2+3y^2=4 each of which makjes an angle 45 degree with the xais is

Question

the locus of mid points of the chords of the ellipse 2x^2+3y^2=4
each of which makjes an angle 45 degree with the xais is

Rahul Raj · Accepted Answer

Dear student

2x2+3y2=4x22+y24/3=1The equation of chord of the ellipse x2a2+y2b2=1 bisected at the point (x1,y1) isxx1a2+yy1b2-1=x12a2+y12b2-1let the midpoint of chord be (h,k)equation isxh2+yk4/3-1=h22+k24/3-1xh2+3yk4=h22+3k24slope =-h/23k/4slope=1 as chord makes π/4 with x-axis-h/23k/4=1-h/2=3k/4-2h=3k2h+3k=0locus is 2x+3y=0

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