If two curves whose equations are `ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0` and `a'x^2 + 2h'xy + b'y^2 + 2g' x + 2f' y + c = 0` intersect in four concyclic point., then prove that a-b/h = a'-b'/h'

If curves a_1 x^2 + 2h_1 xy + b_1 y^2 - 2g_1 x - 2f_y y + c = 0 and a_2 x^2 - 2h_2xy + (a_2 + a_1 - b_1) y^2 - 2g_2 x - 2f_2 y + c = 0 intersect in four concyclic points A, B, C and D . and H be the point ((g_1+g_2)/(a_1 + a_2), (f_1 + f_2)/(a_1 + a_2)) , then (5HA^2 + 7HB^2 + 8HC^2)/(HD^2) = ..

Two conics a_1x^2+2h_1xy + b_1y^2 = c_1, a_2x^2 + 2h_2xy+b_2y^2 = c_2 intersect in 4 concyclic points. Then

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

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

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If ax^2+2hxy+by^2+2gx+2fy+c=0 then find dy/dx

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2.

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

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 .