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Question

The mid-point of the chord 4x - 3y = 5 of the hyperbola 2x23y2=12 is


  1. \)

  2. \)

  3. \)

  4. \)


Solution

The correct option is B

\)


Let the mid-point of the chord is (x1,y1)

Now the equation of chord with given mid-point is

                    T=S1

Here             S2x23y212=0

                    T2xx13yy112=0

   and           S12(x21)3(y21)12=0

     2xx13yy112=2x213y2112

     2x1x3y1y=2x213y21               ..............(1)

But the given equation of the chord is 4x-3y=5                           ...........(2)

Both equation (1)  &   (2) represents same line ratio of their coefficients must be same

2x14=3y13=2x213y215=k      (let's say)

           x1=4k2=2k

                               y1=k

                               2x213y215=k

                              2(2k)23(k)25

                              2×4k23k2=5k

                             8k3k=5

                             5k=5

                             k=1

             Then x1=2×1=2

and y1=1

coordinates of the mid-point of the chord is (2,1)

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