Locus - Cheenta Academy

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July 12, 2020 at 6:00 pm #76116
Lavisha Sharma
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<p>Two gas companies are X and Y, where X is situated at ( 40,0) and Y is situated at (0,30) ( unit =1 km), offer to install equally priced gas furnaces in buyers house. Company X adds a charge of Rs. 40 per km of distance measured along a straight line between its location and buyers house while company Y charges Rs. 60 per km of distance measured in the same way. Then the region where it is cheaper by company X to install the furnace is :</p>
July 13, 2020 at 12:15 pm #76138
Saumik Karfa
Participant
HINT :
Question : Where the cost is same ?
Let's say at a distance $a$ from $Y$ and at a distance $b$ from $X$.
Then $60a = 40 b\Rightarrow \frac ab = \frac 23$
Let $(p,q)$ be a moving point on a plane such that distance from $X$ is $b$ and from $Y$ is $a$.
then $\frac ab =\frac {p^2+(30-q)^2}{(40-p)^2+q^2}= \frac 23$
Locus of $(p,q)$ is a circle.
On that circle cost is same . Where do you think it is cheaper for $X$ ?
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