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)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
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