If the normal to the rectangular hyperbola x y=c2 at the point ' t ' meets the curve again at prime t1 prime then t3 t1 has the value equal to -

Question

If the normal to the rectangular hyperbola x y=c2 at the point ' t ' meets the curve again at prime t1 prime then t3 t1 has the value equal to - (A) 1 (B) -1 (C) 0 (D) none

Tardigrade Admin · Accepted Answer

Equation of normal of rectangular hyperbola xy = c 2 at P ( ct , c / t ) will be y-(c/t)=t2(x-c t) as it also passes through t1 ⇒ c((1/t1)-(1/t))=c t2(t1-t) ⇒ t3 t1=-1

Q. If the normal to the rectangular hyperbola $x y = c^{2}$ at the point ' $t$ ' meets the curve again at $^{'} t_{1}^{'}$ then $t^{3} t_{1}$ has the value equal to -

1

$- 1$

0

none

Equation of normal of rectangular hyperbola $x y = c^{2}$ at $P (c t, c / t)$ will be
$y - \frac{c}{t} = t^{2} (x - c t)$
as it also passes through $t_{1}$
$\Rightarrow c (\frac{1}{t _{1}} - \frac{1}{t}) = c t^{2} (t_{1} - t)$
$\Rightarrow t^{3} t_{1} = - 1$

Q. If the normal to the rectangular hyperbola xy=c2 at the point ' t ' meets the curve again at ′t1​′ then t3t1​ has the value equal to -

1

−1

0

none

Equation of normal of rectangular hyperbola xy=c2 at P(ct,c/t) will be y−tc​=t2(x−ct) as it also passes through t1​ ⇒c(t1​1​−t1​)=ct2(t1​−t) ⇒t3t1​=−1

Q. If the normal to the rectangular hyperbola $x y = c^{2}$ at the point ' $t$ ' meets the curve again at $^{'} t_{1}^{'}$ then $t^{3} t_{1}$ has the value equal to -

$- 1$

Equation of normal of rectangular hyperbola $x y = c^{2}$ at $P (c t, c / t)$ will be
$y - \frac{c}{t} = t^{2} (x - c t)$
as it also passes through $t_{1}$
$\Rightarrow c (\frac{1}{t _{1}} - \frac{1}{t}) = c t^{2} (t_{1} - t)$
$\Rightarrow t^{3} t_{1} = - 1$