The equation of the pair of straight lines perpendicular to the pair $ax^2 + 2hxy + by^2 = 0$ is

The equation of the pair of lines passing through the origin and parallel to the lines $y = m_1x + c_1$ and $y = m_2x + c_2$ is:

If the equation $\lambda x^2 + 2y^2 - 5xy + 5x - 7y + 3 = 0$ represents two straight lines,then the value of $\lambda$ is:

If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of a point which moves such that it is always equidistant from the lines $x+2y+7=0$ and $2x-y+8=0$,then the value of $g+c+h-f$ equals

If the slope of one of the lines represented by $ax^2 + (2a + 1)xy + 2y^2 = 0$ is the reciprocal of the slope of the other,then the sum of the squares of the slopes is

The combined equation of two lines $L$ and $L_1$ is $2x^2+axy+3y^2=0$ and the combined equation of two lines $L$ and $L_2$ is $2x^2+bxy-3y^2=0$. If $L_1$ and $L_2$ are perpendicular,then $a^2+b^2=$