Misc 4 - What points on y-axis whose distance from x/3 + y/4 = 1 - Distance of a point from a line

  1. Chapter 10 Class 11 Straight Lines
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Misc 4 What are the points on the y-axis whose distance from the line ๐‘ฅ/3 + ๐‘ฆ/4 = 1 is 4 units. Let any point on y-axis be P(0, k) Given that distance of point on y-axis from the line ๐‘ฅ/3 + ๐‘ฆ/4 = 1 is 4 units Given line is ๐‘ฅ/3 + ๐‘ฆ/4 = 1 (4๐‘ฅ + 3๐‘ฆ)/12 = 1 4x + 3y = 12 4x + 3y โˆ’ 12 = 0 The above equation is of the form Ax + By + C = 0 Here A = 4, B = 3, and C = โ€“12 We know that Distance of a point (x1, y1) from a line Ax + By + C = 0 is d = |ใ€–๐ด๐‘ฅใ€—_1 + ใ€–๐ต๐‘ฆใ€—_1 + ๐ถ|/โˆš(๐ด^2 + ๐ต^2 ) Given Distance of a point (0, k) from line 4x + 3y โ€“ 12 = 0 is 4 Putting values x1 = 0 , y1 = k , d = 4 & A = 4 , B = 3 , C = โˆ’ 12 So, 4 = |4(0) + 3๐‘˜ + ( โˆ’ 12)|/โˆš((4)^2 + (3)^2 ) 4 = |0 + 3๐‘˜ โˆ’ 12|/โˆš(16 + 9) 4 = |3๐‘˜ โˆ’ 12|/โˆš25 4 = |3๐‘˜ โˆ’ 12|/5 4 ร— 5 = |3๐‘˜โˆ’12| 20 = |3๐‘˜โˆ’12| |3๐‘˜โˆ’12| = 20 3k โ€“ 12 = ยฑ 20 Hence point on y-axis is (0, 32/3) and (0, ( โˆ’ 8)/3)

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