The equations `a^2x^2+2h(a+b)xy+b^2y^2=0` and `ax^2+2hxy+by^2=0` represent.

Options

A. two pairs of perpendicualr straight lines
B. two pairs of parallel straight lines
C. two pairs of straight lines which are eqaully inclined to each other
D. None of these

Answer

C

Explanation

The given equation are `a^2x^2+2h(a+b)xy+b^2y^2=0` ....(i)
and `ax^2+2hxy+by^2=0` .......(ii)
The equation of bisectors of the angles between the lines represented by Eq. (i) is `(x^2-y^2)/(a^2-b^2)=(xy)/(h(a+b))rArr (x^2-y^2)/(a-b)=(xy)/(h)` which is same as equation of the bisectors of angles between the line Eq.(ii). Thus , two pairs of straight line equally inclined to each other .