The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2=12 is

A) (0 , -5/3) B) (2 , 1) C) (5/4 , 0) D) (11/4 , 2)

Question

The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2=12
is
A) (0 , -5/3) B) (2 , 1) C) (5/4 , 0) D) (11/4 , 2)

Vipin Verma · Accepted Answer

The equation of the chord passing through mid-point ( h , k) :
hxa2 -kyb2 =h2a2 -k2b2But 2x2 -3y2 = 12Or x26-y24=1Hence a2 = 6 and
b2 = 4Hence hxa2 -kyb2 =h2a2 -k2b2=hx6 -ky4 =h26 -k24 4hx -6ky =
4h2 -6k2 (1)Putting the value of (h,k) from the options , we have
(2,1) satisfying the equation of the chord 4x-3y = 5

The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2=12 is A) (0 , -5/3) B) (2 , 1) C) (5/4 , 0) D) (11/4 , 2)

The midpoint of the chord 4x-3y=5 of the hyperbola 2x^2-3y^2=12 is

A) (0 , -5/3) B) (2 , 1) C) (5/4 , 0) D) (11/4 , 2)