If the equation `ax^2 +2hxy + by^2 = 0 and bx^2 - 2hxy + ay^2 =0` represent the same curve, then show that `a+b=0`.

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

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

If the pair of lines ax^2-2xy+by^2=0 and bx^2-2xy+ay^2=0 be such that each pair bisects the angle between the other pair , then |a-b| equals to

For the equation ax^(2) +by^(2) + 2hxy + 2gx + 2fy + c =0 where a ne 0 , to represent a circle, the condition will be

Find dy/dx if ax^2+2hxy+by^2=0

If the pair of lines ax^2 +2hxy+ by^2+ 2gx+ 2fy +c=0 intersect on the y-axis then

If the equation ax^2+2bx+c=0 and ax^2+2cx+b=0 b!=c have a common root ,then a/(b+c =

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straights lines, then the product of the perpendicular from the origin on these straight lines, is