The equation $16 x^{2} + y^{2} + 8 x y - 74 x - 78 y + 212 = 0$ represents a

circle

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

parabola

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

ellipse

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

hyperbola

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

Open in App

Solution

The correct option is B parabola
Given equation is $16 x^{2} + y^{2} + 8 x y - 74 x - 78 y + 212 = 0$ ....... $(i)$

General equation of conics is $a x^{2} + b y^{2} + 2 h x y + 2 f x + 2 g y = 0$

Comparing $(i)$ with above equation, we get $a = 16, b = 1, c = 212, h = 4, f = - 37, g = - 39$

so $Δ = a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = - 11881 \neq 0$

Also, $h^{2} = a b = 16$

Hence, given equation represents a Parabola.

Suggest Corrections

Similar questions

The equation $16 x^{2} + y^{2} + 8 x y - 74 x - 78 y + 212 = 0$ represents

Curve $16 x^{2} + 8 x y + y^{2} - 74 x - 78 y + 212 = 0$ represents

16 x^{2} + y^{2} + 5 x y - 74 x - 75 y + 212 = 0

x^{2} y^{2} - 2 x y^{2} - 3 y^{2} - 4 x^{2} y + 8 x y + 12 y = 0

Join BYJU'S Learning Program