Question

The eccentricity of the
conjugate hyperbola
of the hyperbola
x²-3y²=1 is ?
a) 2 b) 4 c) ¾ d) ½

Answer 1

: Let the mid-point of the chord be (h,k)

Then, the equation of the chord of x2 – y2 = a2 is

T = S1

hx – ky = h2 - k2

So, y = h/k x – (h2 - k2)/k and this is tangent of y2 = 4ax

so, – (h2 – k2)/k = a/(h/k)

or -(h2 - k2) = ak2/h

or -h3 + hk2 = ak2

or k2(h-a) = h3

Hence, locus of mid-point is y2(x-a) = x3