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.

Asked by Abhisek | 1 year ago |  102

1 Answer

Solution :-

It is given that

3x + y – 2 = 0 …… (1)

px + 2y – 3 = 0 ….. (2)

2x – y – 3 = 0 …… (3)

By solving equations (1) and (3) we get

x = 1 and y = -1

Here the three lines intersect at one point and the point of intersection of lines (1) and (3) will also satisfy line (2)

p (1) + 2 (-1) – 3 = 0

By further calculation

p – 2 – 3 = 0

So we get

p = 5

Hence, the required value of p is 5.

Answered by Pragya Singh | 1 year ago

Related Questions

Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.

Class 11 Maths Straight Lines View Answer

Prove that the points (2, -1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.

Class 11 Maths Straight Lines View Answer

Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.

Class 11 Maths Straight Lines View Answer

Find the angles between pairs of straight lines 3x – y + 5 = 0 and x – 3y + 1 = 0

Class 11 Maths Straight Lines View Answer

Find the angles between pairs of straight lines 3x + y + 12 = 0 and x + 2y – 1 = 0

Class 11 Maths Straight Lines View Answer