Long range navigation (LORAN) is a radio navigation system developed during world war II the system unable app pilot to guide aircraft by maintaining a constant difference between the aircrafts distances from two fixed points the master station and the slave station right and equation of hyperbola depicted in the following figure.

![](https://assets.chorcha.net/5AHIVnPxM9HitTYo.webp)

Question

Long range navigation (LORAN) is a radio navigation system developed during world war II the system unable app pilot to guide aircraft by maintaining a constant difference between the aircrafts distances from two fixed points the master station and the slave station right and equation of hyperbola depicted in the following figure.

![](https://assets.chorcha.net/5AHIVnPxM9HitTYo.webp)

Accepted Answer

ঘ. x²/14400 - 13y²/129600 = 1

ব্যাখ্যা: চিত্রে দেখানো অধিবৃত্তটির কেন্দ্র মূলবিন্দু $(0,0)$-তে অবস্থিত এবং শীর্ষবিন্দু $(120, 0)$।
সুতরাং, অনুভূমিক অক্ষের অর্ধ-দৈর্ঘ্য, $a = 120$
অতএব, $a^2 = 120^2 = 14400$।

অধিবৃত্তের সাধারণ সমীকরণ:
$$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$
$$\frac{x^2}{14400} - \frac{y^2}{b^2} = 1$$

যেহেতু অধিবৃত্তটি $(140, 60)$ বিন্দুগামী, তাই এই বিন্দুটি সমীকরণটিকে সিদ্ধ করবে:
$$\frac{140^2}{14400} - \frac{60^2}{b^2} = 1$$
$$\Rightarrow \frac{19600}{14400} - 1 = \frac{3600}{b^2}$$
$$\Rightarrow \frac{49}{36} - 1 = \frac{3600}{b^2}$$
$$\Rightarrow \frac{13}{36} = \frac{3600}{b^2}$$
$$\Rightarrow b^2 = \frac{3600 	imes 36}{13} = \frac{129600}{13}$$

অতএব, নির্ণেয় সমীকরণটি হলো:
$$\frac{x^2}{14400} - \frac{13y^2}{129600} = 1$$

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