Question

If the tangent and the normal to a rectangular hyperbola xy=c^2 , at a point , cuts off intercept a1 and a2 on the x axis and b1 , b2 on the y axis then prove that a1a2+b1b2=0

Answer 1

Step-by-step explanation:

Assume rectangular hyperbola is xy=c2

Thus equation of tangent and normal at any point 't' are,

tx+ty=2c and y−tc=t2(x−ct)

Now putting y=0 in both the equation we get, a1=2ct,a2=ct−t3c

and putting x=0 we get, b1=t2c,b2=tc−ct3

⇒a1a2+b1b2=2ct(ct−t3c)+t2c(tc−ct3)=0

Hence. option 'C' is correct.