## Type – I F

When 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 – y_{1} = m (x – x_{1}) 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

- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Find the joint equation of pair of lines through origin, and perpendicular to the lines x + 2y = 19 and 3x + y = 18. (MSB Text)
- 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.
- 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)
- 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)
- 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)

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