Manipal MET2010MathematicsPair of Lines
To the lines a x^2+2 h x y+b y^2=0 the lines a^2 x^2+2 h(a+b) x y+b^2 y^2=0 , are
Options
- Aequally inclined
- Bperpendicular
- Cbisector of the angle
- DNone of the above
Correct answer
A. equally inclined
Step-by-step solution
If the two pairs of straight lines have the same bisectors, then the two pairs are equally inclined. The equation of the bisectors of the angle between the lines given by a x^2+2 h x y+b y^2=0 is x^2-y^2 a-b = x y h ...(i) The equation of the bisectors of the angle between the lines given by a^2 x^2+2 h(a+b) x y+b^2 y^2=0 is x^2-y^2 a^2-b^2 = x y h(a+b) x^2-y^2 a-b = x y h ...(ii) Clearly Eqs. (i) and (ii) are the same. The two pairs of straight lines are equally inclined.