Question

If lines represented by $a{x}^2+2hxy+b{y}^2=0$ makes angles of equal measures with the cordinate axes,then

• A. $ab=\pm 1$
• B. h=0
• C. a=-b
• D. $a=\pm b$

Answer 1

The correct option is B h=0

Writing the equation in slope equation form we get bm${}^2$+2hm+a=0 where m is solpe of line .Since lines make equal angle with coordinate axes ,so if slope of one line is m then slope of other line is (-m).

Thus the sum of roots of equation bm${}^2$+2hm+a=0 must be 0 .

So $\frac{-2h}{b}=0$

$\to h=0$