Question

If the normal to the rectangular hyperbola $xy=4$ at the point $P\left(4\right)$ meets the curve again at the point $Q\left(t_2\right)$, then find the value of $\frac{1}{|t_2|}$

• A. 64.0
• B. 64.00
• C. 64

Answer 1

Answer: (A), (B), (C)

If the normal to the rectangular hyperbola $xy=c^2$
at the point $\left(t_1\right)$ meets the curve again at the point $\left(t_2\right)$, then
$\Rightarrow t_1^3{t}_2=-1$
Normal is drawn at Point $P\left(4\right)$
$\therefore t_1=4$
So, substitute $t_1=4\text{in}{t}_1^3{t}_2=-1$
$\Rightarrow 4^3{t}_2=-1$
$\Rightarrow t_2=\frac{-1}{64}$
$\Rightarrow \frac{1}{|t_2|}=64$