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shivanshi asthana Grade: 11
        

all chords of the curve 3x2-y2-2x+4y=0 that subtends a right angle at the origin pass through a point whose coordinates are.......???

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear shivanshi


let the equation of chord is y=mx+c


so combine equation od pair of straight line that passes through the origin and point of intersection of chord and  curve is


put value of 1 fron the chord  


1=(y-mx)/c


3x2-y2-(2x+4y)(y-mx)/c=0


(3c+2m)x2 + (4m-2)xy +(-c-4)y2 =0


these lines are perpendicular


so a+b =0


  3c +2m -c-4 =0


2=m*1 +c 


compair this with the chord y=mx +c


so it will always pass throug


 (1,2)


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Badiuddin

7 years ago
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