The equation $14 x^{2} - 4 x y + 11 y^{2} - 44 x - 58 + 71 = 0$ represents

A parabola

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An ellipse

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A hyperbola

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A rectangular hyperbola

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Solution

The correct option is B An ellipse
$14 x^{2} - 4 x y + 11 y^{2} - 44 x - 58 y + 71 = 0$
General Equation:-
$A x^{2} + B x y + C y^{2} + D x + E y + F$
$B^{2} - 4 A C = (- 4)^{2} - 4 (14) (11) < 0$
$∴ E l l i p s e$

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