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Question Number 63618 by kaivan.ahmadi last updated on 06/Jul/19

Commented by kaivan.ahmadi last updated on 06/Jul/19

$i d o n t t h i n k$ $i f F^{'} P - F P = 0 < a t h e n P i s n o t i n s i d e$
Commented by kaivan.ahmadi last updated on 06/Jul/19

$e x p l a i n t h e c o n d i t i o n t h a t t h e p o i n t P$ $i s i n s i d e t h e h y p e r b o l a .$
Commented by kaivan.ahmadi last updated on 06/Jul/19

$c a n w e p l o t a t a n g e n t f r o m t h e p o i n t P$ $t o h y p e r b o l a ?$
Commented by Prithwish sen last updated on 06/Jul/19

$If B be any point on hyperbola$ $then F^{'} B ∽ FB = constant (say a)$ $∴ then F^{'} P - FP < a$ $I think .$
Commented by Prithwish sen last updated on 06/Jul/19

$Try$ $F^{'} P - FP > a$
	Answered by MJS last updated on 06/Jul/19

	$hyperbola$ $a, b, e > 0$ $y = \pm \frac{b}{a} \sqrt{x^{2} - a^{2}}$ $∣ F_{1} F_{2} ∣= 2 e$ $H \in hyp : ∣ F_{1} H ∣ - ∣ F_{2} H ∣= 2 a$ $a^{2} + b^{2} = e^{2}$ $if we fix e \Rightarrow b = \sqrt{e^{2} - a^{2}}; b > 0 \Rightarrow a < e$ $y = \pm \frac{\sqrt{(e^{2} - a^{2}) (x^{2} - a^{2})}}{a}$ $for lower values of a the hyperbola becomes$ $steeper (or more open)$ $\Rightarrow for P on a hyperbola inside the given one$ $we would need a higher value of a$ $\Rightarrow ∣ F_{1} P ∣ - ∣ F_{2} P ∣> 2 a$
	Commented by Prithwish sen last updated on 06/Jul/19

	$great sir . Sir please suggest something on$ $the solution of the problem of the comment of 63574$
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