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 two pairs of perpendicular straight lines two pairs of parallel straigh
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
two pairs of perpendicular straight lines
two pairs of parallel straight lines
two pairs of straight lines which are equally inclined to each other
none of these
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
1 Answers
Correct Answer - 3
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.