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Show that all chords of the curve 3x^2-y^ 2-2x + 4y = 0, which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.



30-Nov-2015 2:59 PM
~6

Answers (1)


1
Let the equation of chord be y=mx+c

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

put value of 1 from the chord:  

1=(y-mx)/c

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

(3c+2m)x+ (4m-2)xy +(-c-4)y2 =0

these lines are perpendicular, so a+b =0

3c +2m -c-4 =0

2=m*1 +c 

compare this with the chord y=mx +c

so it will always pass through the fixed point:

 (1,2)



01-12-2015 17:32
~20

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