The equation to the lines passing through the origin and inclined at angles $\frac{π}{4}$ and $\frac{3 π}{4}$ to x- axis is

x^{2} + 2 y^{2} = 0

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x^{2} - y^{2} = 0

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y^{2} = 2 x^{2}

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2 x^{2} + y^{2} = 0

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Solution

The correct option is C $x^{2} - y^{2} = 0$
$y = tan \frac{π}{4} x$ , and
$y = tan \frac{3 π}{4} x$
$y = x$ and $y = - x$
So, pair of straight line of $y = x$ and $y + x = 0$ is
$(y - x) (y + x) = 0$
$\Rightarrow y^{2} - x^{2} = 0$
Or $\Rightarrow x^{2} - y^{2} = 0$

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The equation to the lines passing through the origin and inclined at angles π4 and 3π4 to x- axis is

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The equation to the lines passing through the origin and inclined at angles $\frac{π}{4}$ and $\frac{3 π}{4}$ to x- axis is

The correct option is C $x^{2} - y^{2} = 0$
$y = tan \frac{π}{4} x$ , and
$y = tan \frac{3 π}{4} x$
$y = x$ and $y = - x$
So, pair of straight line of $y = x$ and $y + x = 0$ is
$(y - x) (y + x) = 0$
$\Rightarrow y^{2} - x^{2} = 0$
Or $\Rightarrow x^{2} - y^{2} = 0$