The equation `a^2x^2+2h(a+b)x y+b^2y^2=0` and `a x^2+2h x y+b y^2=0` represent (a)two pairs of perpendicular straight lines (b)two pairs of parallel straight lines (c)two pairs of straight lines which are equally inclined to each other (d)none of these

Options

A. two pair of perpendicular straight lines
B. two pairs of parallel straight lines
C. two pairs of straight lines which are equally inclined to each other
D. None of these

Answer

3

Explanation

The given equations are
`a^(2)x^(2)+2h(a+b)xy+b^(2)y^(2)=0` (1)
and `ax^(2)+2hxy+by^(2)=0` (2)
The equation of the bisectors of the angles between the lines represented by (1) is
`(x^(2)-y^(2))/(a^(2)-b^(2))=(xy)/(h(a+b))`
or `(x^(2)-y^(2))/(a-b)=(xy)/(h)`
which is the same as the equation of bisectors of the angles between the line pair (2). thus , two line pairs are equally inclined to each other.