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

a circle

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a parabola

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an ellipse

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a hyperbola

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Solution

The correct option is B
a parabola

Comparing the given equation with $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0,$ we get :

a=16,b=1, h=4

We have : $h^{2} = 16 = a b$

Thus, the given equation represents a parabola.

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Similar questions

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

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

x = \frac{t}{4}, y = \frac{t^{2}}{4}

x = 2 (cos t + sin t), y = 5 (cos t - sin t)

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