Question

An oil tanker is to travel from Tunisia to Italy as shown in fig. The captain wants to travel a course that is always the same distance from a point on the coast of Sardinia as it is from a point on the coast of Sicily (both denoted in *)
Choose the correct options -

• A. Tanker will be at distance $\sqrt{2}$ from * points when it reaches position 1.
• B. Tanker will be at distance $\sqrt{10}$ from * points when it reaches position 2.
• C. Tanker will be at distance $\sqrt{10}$ from * points when it reaches position 1.
• D. Tanker will be at distance $\sqrt{2}$ from * points when it reaches position 2.

Answer 1

Answer: (A), (B)

The correct options are
A Tanker will be at distance $\sqrt{2}$ from * points when it reaches position 1.
B Tanker will be at distance $\sqrt{10}$ from * points when it reaches position 2.

Assuming position 1 as origin.
Coordinates of Sardinia $=(-1,1)$
Distance of Sardinia from position 1 $=\sqrt{(-1{)}^2+(1{)}^2}=\sqrt{2}$
Similarly distance of Sieily $=\sqrt{1^2+(-1{)}^2}=\sqrt{2}$
When tanker reaches position 2 assuming position 2 as origin co-ordinates of Sardinia $=(-3,-1)$.
Distance of Sardinia from position 2 $=\sqrt{(-3{)}^2+(-1{)}^2}=\sqrt{10}$
Similarly distance of Sielily $=\sqrt{(-1{)}^2+(-3{)}^2}=\sqrt{10}$