If the equation `ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0` resents a pair of parallel lines then prove that

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents a pair of parallel lines, then

If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of parallel lines, prove that h=sqrt(ab) and gsqrt(b)=fsqrt(a)or (h=-sqrt(ab)and gsqrt(b)=-fsqrt(a)) . The distance between them is 2sqrt((((g^2-ac))/(a(a+b)))) .

IF the equation x^(2) + y^(2) + 2gx + 2fy + 1 = 0 represents a pair of lines, then

If the equation ax ^(2) - 6xy +y ^(2) + 2gx + 2fy + x =0 represents a pair of lines whose slopes are m and m^(2), then sum of all possible values of |(3a)/(10)| is "______"

the equation ax^(2)+ 2hxy + by^(2) + 2gx + 2 fy + c=0 represents an ellipse , if

If the equation hxy + gx + fy + c = 0 represents a pair of straight lines, then

If the equation ax^(2)+2hxy+by^(2)+25x+2fy+c=0 represents a pair of straight lines,prove that the third pair of straight lines (excluding xy=0) passing through the points where these meet the axes is ax^(2)2hxy+by^(2)+2gx+2fy+c+(4fg)/(c)*xy=0