Ex 10.3, 5 - Find points on x-axis, whose distances from - Distance of a point from a line

  1. Class 11
  2. Important Question for exams Class 11
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Ex 10.3, 5 Find the points on the x-axis, whose distances from the line ๐‘ฅ/3 + ๐‘ฆ/4 = 1 are 4 units. We need to find point on the x-axis Let any point on x-axis be P(x, 0) Given that perpendicular distance from point P(x, 0) from given line ๐‘ฅ/3 + ๐‘ฆ/4 = 1 is 4 Simplifying equation of line ๐‘ฅ/3 + ๐‘ฆ/4 = 1 (4๐‘ฅ + 3๐‘ฆ )/12 = 1 4x + 3y = 12 4x + 3y โ€“ 12 = 0 We know that Perpendicular distance from point (x, y) to the line Ax + By + C = 0 is d = |๐ด๐‘ฅ1 + ๐ต๐‘ฆ1 + ๐‘|/โˆš(๐ด^2 + ๐ต^2 ) Given perpendicular distance of point P(x, 0) from line 4x + 3y โ€“ 12 = 0 is 4 Here x1 = x , y1 = 0 & A = 4 , B = 3 , C = โˆ’ 12 & d = 4 Putting values 4 = |4(๐‘ฅ) + 3(0) โˆ’ 12|/โˆš(ใ€–(4)ใ€—^2 + ใ€–(3)ใ€—^2 ) 4 = |4๐‘ฅ โˆ’ 12|/โˆš(16 + 9) 4 = |4๐‘ฅ โˆ’ 12|/โˆš25 4 = |4๐‘ฅ โˆ’ 12|/5 4 ร— 5 = |4๐‘ฅ โˆ’ 12| 20 = |4๐‘ฅ โˆ’ 12| |4๐‘ฅ โˆ’ 12| = 20 4x โ€“ 12 = ยฑ 20 Thus, 4x โˆ’ 12 = 20 or 4x โˆ’ 12 = โˆ’ 20 Thus, x = 8 or x = โˆ’ 3 Hence the required points on x-axis are (8, 0) & ( โˆ’ 2, 0)

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