1. 1B_Ch10(1) A B C D E G F 60 o 30 o

2. 1 Joint equation of pair of straight lines 2 Angle between a pair of straight lines 3 Condition of parallelism and perpendicularity 4 Joint equation of angle bisectors 5 Joint equation of lines joining origin to the intersection of a line and a curve CONTENTS

3. The equation ax 2 + 2hxy + by 2 + 2gx + 2fy + c = 0 represents a second degree equation where a, h, b doesn’t vanishes simultaneously. This equation represents a pair of straight lines if abc + 2fgh– af 2 – bg 2 – ch 2 = 0

4. Any two lines through the Origin may be written as and where and are their gradients. So or must represent the pair. The general form of this equation is given by: giving

5. Therefore, homogeneous part of the general second degree equation i.e. ax 2 + 2hxy + by 2 = 0 represents the pair of straight lines passing through the origin. O A B X Y

6. Angle between a pair of straight lines If is the angle between a pair of straight lines given by then,

7. The lines represented by pair of straight lines are parallel if The lines represented by pair of straight lines are prependicular if h 2 =ab Condition of parallelism and perpendicularity

8. The Equation Of The Angle Bisectors Joint equation of angle bisectors of pair of lines is given by:

9. To find joint equation of lines joining origin to the intersection of a line and a curve which is an homogeneous equation of second degree. is given by:

10. By: Kunjan Gupta Pggcg, Sector 11, Chd.