The equation 16x² + y² + 8xy − 74x − 78y + 212 = 0 represents
(a) a circle
(b) a parabola
(c) an ellipse
(d) a hyperbola

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Solution

(b) a parabola
Comparing the given equation with ax² + by² + 2hxy + 2gx+2fy + 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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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} + 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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