If the normal at the point $^{'} t_{1}^{'}$ to the rectangular hyperbola $x y = c^{2}$ meets it again at the point $^{'} t_{2}^{'}$ then the value of $t_{1} t_{2}$ is:

- t_{1}^{- 1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- t_{1}^{- 2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- t_{1}^{- 3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- t_{1}^{- 4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $- t_{1}^{- 2}$
Equation of normal of $x y = c^{2} a t t_{1}$ is
$y - \frac{c}{t_{1}} = t_{1}^{2} (x - c t_{1})$
As it also passes through $t_{2}$ ,
$\frac{c}{t_{2}} - \frac{c}{t_{1}} = t_{1}^{2} (c t_{2} - c t_{1})$
$\Rightarrow t_{1} t_{2} = - t_{1}^{- 2}$
Hence, option 'B' is correct.

Suggest Corrections

Similar questions

The normal to the rectangular hyperbola $x y = c^{2}$ at the point ' $t_{1}$ ' meets the curve again at the point ' $t_{2}$ '. Then the value of $t_{1}^{3} t_{2}$ is

Q. If a normal to the hyperbola

x y = c^{2}

(c t_{1}, \frac{c}{t_{1}})

meets the curve again at

(c t_{2}, \frac{c}{t_{2}})

then:

Q. If normal to the rectangular hyperbola

x y = 4

at the point

t_{1} (= 4)

meets the curve again at the point

t_{2}

, then

\frac{1}{| t_{2} |} =

Q. If normal to the rectangular hyperbola

x y = 4

at the point

t_{1} (= 4)

meets the curve again at the point

t_{2}

, then

\frac{1}{| t_{2} |} =

Q. The normal to the rectangular hyperbola

x y = - c^{2}

at the point

^{'} t_{1}^{'}

meets the curve again at the point

^{'} t_{2}^{'}

. The value of

t_{1}^{3} \cdot t_{2}

Join BYJU'S Learning Program

If the normal at the point ′t′1 to the rectangular hyperbola xy=c2 meets it again at the point ′t′2 then the value of t1t2 is:

The correct option is B −t−21Equation of normal of xy=c2att1 isy−ct1=t21(x−ct1)As it also passes through t2,ct2−ct1=t21(ct2−ct1)⇒t1t2=−t−21Hence, option 'B' is correct.

If the normal at the point $^{'} t_{1}^{'}$ to the rectangular hyperbola $x y = c^{2}$ meets it again at the point $^{'} t_{2}^{'}$ then the value of $t_{1} t_{2}$ is: