Normal drawn to the hyperbola x y=1 at point A(t1), where it meets the hyperbola again at B(t2), then

Question

Normal drawn to the hyperbola x y=1 at point A(t1), where it meets the hyperbola again at B(t2), then (A) t13 t2=1 (B) t13 t2=-1 (C) t1 t23=1 (D) t1 t23=-1

Tardigrade Admin · Accepted Answer

y =(1/ x ) ( dy / dx )=(-1/ x 2) Equation of normal A ( t 1) and A ( t 2) ((1/t2)-(1/t1)/t2-t1)=t12 ⇒ t13 t2=-1

Q. Normal drawn to the hyperbola $x y = 1$ at point $A (t_{1})$ , where it meets the hyperbola again at $B (t_{2})$ , then

$t_{1}^{3} t_{2} = 1$

$t_{1}^{3} t_{2} = - 1$

$t_{1} t_{2}^{3} = 1$

$t_{1} t_{2}^{3} = - 1$

$y = \frac{1}{x}$
$\frac{d y}{d x} = \frac{- 1}{x ^{2}}$
Equation of normal $A (t_{1})$ and $A (t_{2})$
$\frac{\frac{1}{t _{2}} - \frac{1}{t _{1}}}{t _{2} - t _{1}} = t_{1}^{2}$
$\Rightarrow t_{1}^{3} t_{2} = - 1$

Q. Normal drawn to the hyperbola xy=1 at point A(t1​), where it meets the hyperbola again at B(t2​), then

t13​t2​=1

t13​t2​=−1

t1​t23​=1

t1​t23​=−1