A company situated at (2,0) in the XY-plane c | vedclass

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(B) Let $P(x, y)$ be any point in the $XY$-plane.According to the problem,the cost of the first company is $2 	imes PA$ and the second is $3 	imes P

Vedclass · Accepted Answer

the outside of the circle $(x+1.6)^2+(y-5.4)^2=18.72$

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(B) Let $P(x, y)$ be any point in the $XY$-plane.According to the problem,the cost of the first company is $2 	imes PA$ and the second is $3 	imes PB$.We want the region where it is cheaper to use the first company,so $2 PA Squaring both sides,we get $4 PA^2 Substituting the coordinates $A(2, 0)$ and $B(0, 3)$,we have $4[(x-2)^2 + y^2] Expanding this,$4(x^2 - 4x + 4 + y^2) $4x^2 - 16x + 16 + 4y^2 Rearranging terms,$5x^2 + 5y^2 + 16x - 54y + 65 > 0$.Dividing by $5$,$x^2 + y^2 + 3.2x - 10.8y + 13 > 0$.Completing the square,$(x^2 + 3.2x + 1.6^2) + (y^2 - 10.8y + 5.4^2) > -13 + 2.56 + 29.16$.$(x + 1.6)^2 + (y - 5.4)^2 > 18.72$.This represents the region outside the circle $(x + 1.6)^2 + (y - 5.4)^2 = 18.72$.

$A$ company situated at $(2,0)$ in the $XY$-plane charges $RS. 2$ per $km$ for delivery. $A$ second company at $(0,3)$ charges $RS. 3$ per $km$ for delivery. The region of the plane where it is cheaper to use the first company is

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