There are two radar sites located along a coastline at $A$ and $B$. They are tracking a ship tha

Question

There are two radar sites located along a coastline at $A$ and $B$. They are tracking a ship that is traveling on a hyperbolic path with centre at the origin as shown in the diagram.These $2$ radars are each located $150$ metres from the centre of the hyperbolic path. The shortest distance between the ship and the centre is $90$ metres. When the ship is due north of the radar $B$, it is $340$ metres away from radar $A$. Find the equation of the hyperbola on which the ship sails.[3] If the ship is ${360}$ metres from radar ${B}$ and is travelling on the path nearer to radar ${A}$, find the shortest distance between the ship and the coastline.[3]

Accepted Answer

(i) $\frac{x^2}{90^2}-\frac{y^2}{120^2}=1$; (ii) shortest distance $48\sqrt{14}$ m

HCI Graphing Techniques Tutorial Q9

HCI Graphing Techniques Tutorial Q9

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