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Question

The distance of P(x,y) from A(5,1) and V(1,5) are equal then xy=pq. Find the value of p+q

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Solution

Distance between two points (x1,y1) and (x2,y2) can be calculated using the formula (x2x1)2+(y2y1)2
Given,

Distance between the points (x,y);(5,1)= Distance between (x,y);(1,5)

(5x)2+(1y)2=(1x)2+(5y)2

(5x)2+(1y)2=(1x)2+(5y)2

52+x210x+12+y22y=12+x2+2x+52+y210y

10x2y=+2x10y

12x=8y

xy=23

Hence, p+q=5.


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