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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.......???

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.......???

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

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

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