You visited us 1 times! Enjoying our articles? Unlock Full Access!

Family of Straight Lines

A general equ...

Question

A general equation of second degree i.e., $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ always represents a pair of straight lines.

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False

Suggest Corrections

Similar questions

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

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

a x^{2} - 2 h x y + b y^{2} + 2 g x + 2 f y + c + \frac{4 f g}{c} x y = 0

6 x^{2} - 42 x y + 60 y^{2} - 11 x + 10 y + λ = 0

λ = 10.

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

a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0

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

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

tan θ = \frac{2 \sqrt{h^{2} - a b}}{a + b}

a + b = 0

\frac{x^{2} - y^{2}}{a - b} = \frac{x y}{h}

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

△ = 0

∣ ∣ ∣ ∣ \begin{matrix} a & h & g h & b & f g & f & c \end{matrix} ∣ ∣ ∣ ∣ = 0

a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0

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

Join BYJU'S Learning Program