NCERT Class XI Mathematics - Straight Lines - Solutions
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Question : 62
Total: 74
Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
Solution:
The given equation of lines are
3x + y – 2 = 0 ... (i)
px + 2y – 3 = 0 ... (ii)
2x – y – 3 = 0 ... (iii)
(i), (ii) and (iii) are concurrent if they intersect at one point. Firstly, we find the intersection point of (i) & (ii).
on solving (i) and (ii), we get x = 1, y = –1.
Hence, (i), (ii) and (iii) all three lines are concurrent if the point (1, – 1) lies in the (ii).
i.e., p – 2 – 3 = 0 ⇒ p = 5.
3x + y – 2 = 0 ... (i)
px + 2y – 3 = 0 ... (ii)
2x – y – 3 = 0 ... (iii)
(i), (ii) and (iii) are concurrent if they intersect at one point. Firstly, we find the intersection point of (i) & (ii).
on solving (i) and (ii), we get x = 1, y = –1.
Hence, (i), (ii) and (iii) all three lines are concurrent if the point (1, – 1) lies in the (ii).
i.e., p – 2 – 3 = 0 ⇒ p = 5.
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