If one of the lines denoted by the line pair `a x^2+2h x y+b y^2=0` bisects the angle between the coordinate axes, then prove that `(a+b)^2=4h^2`

Options

A. `(a-b)^2=h^2`
B. `(a+b)^2=h^2`
C. `(a-b)^2=4h^2`
D. `(a+b)^2=4h^2`

Answer

D

Explanation

Clearly, `y=x` is one of the lines given by the equation `ax^2+2hxy+by^2=0`
`therefore ax^2+2hx^2+bx^2=0`
`rArr a+b=-2h`
`therefore (a+b)^2=4h^2` .