NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 73

Total: 74

If sum of the perpendicular distances of a variable point P(x, y) from the lines x + y – 5 = 0 and 3x – 2y + 7 = 0 is always 10. Show that P must move on a line.

Solution:

The given equations of lines are
x + y – 5 = 0 ... (i)
3x – 2y + 7 = 0 ... (ii)
According to question,
⇒

|x+y−5|

√12+12

|3x−2y+7|

√32+22

= 10 ⇒

±(x+y−5)

√2

(3x−2y+7)

√13

= 10 which shows a set of four lines.

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