Question 42 Find a relation between x and y such that the point (x,y) is equidistant from the Country C and Country D (a) x − y = 2 (b) x + y = 2 (c) 2x − y = 0 (d) 2x + y = 2
Let Point P(x, y) be the required point
Since point P (x, y) is equidistant from C (7, 1) and D (3, 5)
CP = DP
√(( 𝑥 −7)2+(𝑦−1)2) = √((𝑥−3)2+(𝑦−5)2)
Squaring both sides
( 𝒙 −𝟕)𝟐+(𝒚−𝟏)𝟐 =(𝒙−𝟑)𝟐+(𝒚−𝟓)𝟐
𝑥^2+49−14𝑥+𝑦^2+1−2𝑦=𝑥^2+9−6𝑥+𝑦^2+25−10𝑦
49−14𝑥+1−2𝑦=9−6𝑥+25−10𝑦
−14𝑥−2𝑦+50=−6𝑥−10𝑦+34
0=−6𝑥−10𝑦+34+14𝑥+2𝑦−50
0=−6𝑥+14𝑥−10𝑦+2𝑦+34−50
0=8𝑥−8𝑦−16
16=8𝑥−8𝑦
𝟖𝒙−𝟖𝒚=𝟏𝟔
Dividing by 8 both sides
𝒙−𝒚=𝟐
So, the correct answer is (a)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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