The axis of the parabola $x^{2} + 2 x y + y^{2} - 5 x + 5 y - 5 = 0$ is

x + y = 0

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x + y - 1 = 0

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x - y + 1 = 0

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x - y = \frac{1}{\sqrt{2}}

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Solution

The correct option is A $x + y = 0$
Axis of a parabola is the line about which it is symmetric. Hence, for axis of a parabola, put the quadratic (square) term equal to zero.

$x^{2} + 2 x y + y^{2} - 5 x + 5 y - 5 = 0$
$\Rightarrow (x + y)^{2} - 5 (x - y) - 5 = 0$
Therefore, equation of the axis of the parabola is $x + y = 0$

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x^{2} + y^{2} + 3 x + 4 y - 5 = 0

x^{2} + y^{2} - 5 x + 5 y - 6 = 0

x^{2} + y^{2} + 3 x + 4 y - 5 = 0

x^{2} + y^{2} - 5 x + 5 y - 6 = 0

(0, 0)

x - y + 1 = 0

The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x-y+1=0 is

y^{2} = 5 x

x^{2} = 5 y

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