  Question

# The mid-point of the chord 4x - 3y = 5 of the hyperbola 2x2−3y2=12 is \) \) \) \)

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             S≡2x2−3y2−12=0                     T≡2xx1−3yy1−12=0    and           S1≡2(x21)−3(y21)−12=0 ⇒     2xx1−3yy1−12=2x21−3y21−12 ⇒     2x1x−3y1y=2x21−3y21               ..............(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=2x21−3y215=k      (let's say) ⇒           x1=4k2=2k                                y1=k                                2x21−3y215=k                               2(2k)2−3(k)25                               2×4k2−3k2=5k                              8k−3k=5                              5k=5                              k=1              Then x1=2×1=2 and y1=1 coordinates of the mid-point of the chord is (2,1)  Suggest corrections   