Show that the line y $=$ mx bisects the angle between the lines $a x^{2} + 2 h x y + b y^{2} = 0$ if $h (1 - m^{2}) - m (a - b) = 0$ .

Open in App

Solution

Bisectors of the given pair of lines is $\frac{x^{2} - y^{2}}{a - b} = \frac{x y}{h}$ . If $y = m x$ be one of the bisectors, then it will satisfy above.
$∴ \frac{x^{2} - m^{2} x^{2}}{a - b} = \frac{x \cdot m x}{h}$
or $h (1 - m^{2}) - m (a - b) = 0$ .

Suggest Corrections

Similar questions

If y = mx be one of the bisectors of the angle between the lines $a x^{2} - 2 h x y + b y^{2} = 0$ , then

y = m x

a x^{2} + 2 h x y + b y^{2} = 0

m

a x^{2} + 2 h x y + b y^{2} = 0

(a - b)^{2} = 4 h^{2}

a x^{2} + 2 h x y + b y^{2} = 0

a x^{2} + 2 h x y - a y^{2} = 0

b x^{2} + 2 g x y - b y^{2} = 0

Join BYJU'S Learning Program