## Type – I FWhen Point and Two Other Lines are Given

Problems in RED colour are for Last Minute Revision (LMR)

Notes :
1. Slope of ax + by + c = 0 is (b ≠0)        i.e. 2. When two lines are parallel their slopes are equal.
3. When two lines are perpendicular product of their slopes is -1, Thus, If slope one line is m, then slope of a line perpendicular to it is ALGORITHM :
1. Find slopes of given line using formula given in point 1 of notes.
2. Find the slopes of required lines forming pair using relations given in points 2 and 3 of notes.
3. Use slope point form y – y1 = m (x – x1) to find equations of given lines. If Lines are passing through origin use y = mx form.
4. Write equations of lines in the form u = 0 and v = 0.
5. Find u.v = 0.
6. Simplify the L.H.S. of joint equation.

### Problems for Practice

1. Find the joint equation of a pair of lines through the origin such that one is parallel to x + 2y = 5 and other is perpendicular to 2x – y + 3 = 0.
2. Find the joint equation of a pair of lines through the origin such that one is parallel to 2x + y – 5 = 0 and other is perpendicular to 3x – 4y + 7 = 0.
3. Find the joint equation of a pair of lines through the origin such that one is parallel to 3x – y = 7 and other is perpendicular to 2x + y = 8.
4. Find the joint equation of pair of lines through origin, one of which is parallel to and another is perpendicular to the line 2x + 3y – 2 = 0.
5. Find the joint equation of pair of lines through origin, one of which is parallel to and another is perpendicular to the line 5x + 3y = 7.
6. Find the joint equation of a pair of lines through the origin such that one is parallel to and other is perpendicular to x + 2y + 1857 = 0.
7. Find the joint equation of pair of lines through origin, and perpendicular to the lines x + 2y = 19 and 3x + y = 18. (MSB Text)
8. Find the joint equation of a pair of lines through the point (3, 4) and such that one is parallel to 2x + 3y + 7 = 0 and other is perpendicular to 3x – 5y = 8.
9. Find the joint equation of a pair of lines through the point (- 1, 2) and perpendicular to lines x + 2y + 3 = 0 and 3x – 4y – 5 = 0. (MSB Text)
10. Find the joint equation of a pair of lines through the point (3, 2) one of which is parallel to x – 2y = 2 and other is perpendicular to y = 3. (MSB Text)
11. Find the joint equation of a pair of lines through the point (1, 2) and perpendicular to both the lines 3x + 2y – 5 = 0 and 2x – 5y + 1 = 0. (MSB Text)