If the normal to the given hyperbola at the point `(c t , c/t)` meets the curve again at `(c t^(prime), c/t^(prime)),` then `t^3t^(prime)=1` (b) `t^3t^(prime)=-1` `tt^(prime)=1` (d) `tt^(prime)=-1`

Options

A. `t^(2)t'=-1`
B. `t^(3)t'=-1`
C. `tt'=-1`
D. None of these

Answer

B

Explanation

Equation of normal at `(ac, c//at)` is `yt-xt^(3)-c+ct^(4)=0`
If it passes through any point say Q having its coordinates as 't' i.e., (ct' c/t')
The coordinates must satisfy the equation
Hence, we get `©/(t').t-ct't^(3)-c+ct^(4)=0`
`impliest-t'^(2)t^(3)-t'+t't^(4)=0`
Factorizing, we get, `(t't^(3)+1)(t-t'=0`
Hence `t't^(3)+1=0 or t't^(3)=-1`
as `tnet'`