If the three ellipses `(x^(2))/(a_(i)^(2))+(y^(2))/(b_(i)^(2))=1`,i=1,2,3 have a common tangent,then the value of `|[a_(1)^(2),b_(1)^(2),1],[a_(2)^(2),b_(2)^(2),1],[a_(3)^(2),b_(3)^(2),1]|`

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

If the points (a_(1),b_(1))m(a_(2),b_(2))" and " (a_(1)-a_(2),b_(2)-b_(2)) are collinear, then prove that a_(1)/a_(2)=b_(1)/b_(2)

the value of the determinant |{:((a_(1)-b_(1))^(2),,(a_(1)-b_(2))^(2),,(a_(1)-b_(3))^(2),,(a_(1)-b_(4))^(2)),((a_(2)-b_(1))^(2),,(a_(2)-b_(2))^(2) ,,(a_(2)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(3)-b_(1))^(2),,(a_(3)-b_(2))^(2),,(a_(3)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(4)-b_(1))^(2),,(a_(4)-b_(2))^(2),,(a_(4)-b_(3))^(2),,(a_(4)-b_(4))^(2)):}| is

Find the values of x,y for following cuestion (a_(3)-a_(2))x+(b_(3)-b_(2))y=((a_(2)^(2)+b_(2)^(2))-(a_(3)^(2)+b_(3)^(2)))/(2) and (a_(3)-a_(1))x+(b_(3)-b_(1))y=((a_(1)^(2)+b_(1)^(2))-(a_(3)^(2)+b_(3)^(2)))/(2)

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is

Let the sequence a_(1),a_(2),a_(3),...,a_(n) from an A.P.Then the value of a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-...+a_(2n-1)^(2)-a_(2n)^(2) is (2n)/(n-1)(a_(2n)^(2)-a_(1)^(2))(b)(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))(n)/(n+1)(a_(1)^(2)-a_(2n)^(2))(d)(n)/(n-1)(a_(1)^(2)+a_(2n)^(2))

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is