The conic represented by the equation $x^{2} + y^{2} - 2 x y + 20 x + 10 = 0$ is

a parabola

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an ellipse

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a hyperbola

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a pair fo straight line

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Solution

The correct option is A a parabola
On compairing the given eqaution with the equation
$a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ we get
$a = b = 1, h = - 1, c = 10, g = 10$ and $f = 0$
$∴ Δ = a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 10 - 100 - 10 = - 100 \neq 0$
and $h^{2} = 1 = a b$
Hence given equation represents a parabola

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