Pair of lines passing though origin

Q.

Find the equation of conjugate hyperbola whose equations of asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and hyperbola passes through (1, -1).

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Q.

If two of the three lines represented by the equation $a{x}^3+b{x}^{2}y+cx{y}^2+d{y}^3=0$ are perpendicular, then

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Q.

The combined equation of straight lines joining the origin to the points of intersection the line y=2x+1 with the curve $x^2+y^2+2xy+4=0$ is given by

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Q.

Find the equations of the lines which cut-off intercepts on the axes whose sum and product are 1 and - 6 respectively.

Q.

If the line $ky-2x-k^2+2h=0\&$ parabola $x^2=4y$ touches each other, then

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