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

Two conics a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=c_(1),a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=c_(2) intersect in 4 concyclic points.Then

Statement 1 : If two conics a_(1)x^(2)+ 2h_(1)xy+b_(1)^(2)=c_(1) , a_(2)x^(2) +2h_(2) xy +b_(2)y^(2) =c_(2) intersect in 4 concyclic points, then ( a_(1) -b_(1)) h_(2)=(a_(2)-b_(2))h_(1) . Statement 2 : For a conic to be a circle, coefficient of x^(2) = coefficient of y^(2) and coefficient of xy =0.

Statement 1 : If two conics a_(1)x^(2)+ 2h_(1)xy+b_(1)^(2)=c_(1) , a_(2)x^(2) +2h_(2) xy +b_(2)y^(2) =c_(2) intersect in 4 concyclic points, then ( a_(1) -b_(1)) h_(2)=(a_(2)-b_(2))h_(1) . Statement 2 : For a conic to be a circle, coefficient of x^(2) = coefficient of y^(2) and coefficient of xy =0.

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) = ..

If the two lines a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0 cut the co-ordinates axes in concyclic points. Prove that a_1a_2 = b_1b_2

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

Find the condition for the two concentric ellipses a_1x^2+\ b_1y^2=1\ a n d\ a_2x^2+\ b_2y^2=1 to intersect orthogonally.

If the pair of lines a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 and a_(2)x^(2)+2h_(2)xy+b_(3)y^(2)=0 have one line in common then show that (a_(1)b_(2)-a_(2)b_(1))^(2)+4(a_(1)h_(2)-a_(2)h_(1))(b_(1)h_(2)-b_(2)h_(1))=0

If a_1x^2 + b_1 x + c_1 = 0 and a_2x^2 + b_2 x + c_2 = 0 has a common root, then the common root is