Question

What is the equation of angle bisectors of a pair of straight lines given by (x+4y-12)(x-4y+4)=0

Answer 1

Step-by-step explanation:

) The angle between two intersecting straight lines means the measure of the acute angle between the lines. (iii) The formula tan θ = ± m2−m11+m1m2 cannot be used to find the angle between the lines AB and CD, if AB or CD is parallel to y-axis.

Answer 2

Let ax2 + 2hxy + by2 = 9 represent lines

y – m1x = 0 and y – m2x = 0

 

Let P(α, ß) be any point on one of bisectors.

 

⇒ (ß–m1α)/√1+m12 = + ß–m2α/√1+m22

 

⇒ (1 + m22) (ß – m1α)2 – (1 + m12) (ß – m2α)2 = 0

 

⇒ Locus of P(α, ß) is

 

x2 – y2 = 2hxy 1–m1m2/m1+m1

 

⇒ x2–y2/a–b = xy/h; is required equation of angle bisectors   …… (1)