[" 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.

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

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

8.If the lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 cuts the coordinate axes in concyclic points then

If one of the lines given by the equation a_(1)x^(2)+2h_(1)xy+b_(1)y^(2)=0 coincides with one of the lines given by a_(2)x^(2)+2h_(2)xy+b_(2)y^(2)=0 and the other lines represented by them are perpendecular then prove that. h_(1)((1)/(a_(1))-(1)/(b_(1)))=h_(2)((1)/(a_(2))-(1)/(b_(2)))

The line a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 are perpendicular if: