Questions in pair-st-lines

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The equation ${{(x+y)}^{2}}-({{x}^{2}}+{{y}^{2}})=0$ represents
If the slope of one of the lines represented by $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$ be the square of the other, then
Two lines represented by equation ${{x}^{2}}+xy+{{y}^{2}}=0$ are
If the equation $hxy+gx+fy+c=0$ represents a pair of straight lines, then
The equation of pair of straight lines perpendicular to the pair $a{{x}^{2}}+2hxy+b{{y}^{2}}=0$ is
The values of h for which the equation $3{{x}^{2}}+2hxy-3{{y}^{2}}-40x+30y-75=0$ represents a pair of straight lines, are
The equation of lines passing through the origin and parallel to the lines $y={{m}_{1}}x+{{c}_{1}}$ and $y={{m}_{2}}x+{{c}_{2}}$ is
The equation of the lines represented by the equation $ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0$ are
The equation ${{(x-5)}^{2}}+(x-5)\,(y-6)\,-2\,{{(y-6)}^{2}}=0$ represents
A second degree homogenous equation in x and y always represents

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