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प्रश्न
Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).
उत्तर
Given : MR = MT
∴ MR2 = MT2
(x - 0)2 + (y - 9)2 = (x - 14)2 + (y - 11)2
x2 + y2 + 81 - 18y = x2 + 196 - 28x + y2 + 121 - 22y
81 - 18y = 196 - 28x +121 - 22y
28 x - 18 y + 22 y = 196 + 121 - 81
28 x + 4y = 236
7x + y - 58 = 0
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
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- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
