If the parabolas `y^(2)=4axandy^(2)=4c(x-b)` have a common normal other than x-axis (a,b,c being distinct positive real numbers), then prove that `(b)/(a-c)gt2`.

If the parabolas y^2=4a x and y^2=4c(x-b) have a common normal other than the x-axis (a , b , c being distinct positive real numbers), then prove that b/(a-c)> 2.

If the parabolas y^2=4a x and y^2=4c(x-b) have a common normal other than the x-axis (a , b , c being distinct positive real numbers), then prove that b/(a-c)> 2.

If a,b,c are distinct positive real numbers, then

The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common normal other than X-axis (agt0,cgt0) is

If a,b,c are three distinct positive real numbers in G.P., than prove that c^2+2ab gt 3ac .

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3ac

If the parabols y^(2) = 4kx (k gt 0) and y^(2) = 4 (x-1) do not have a common normal other than the axis of parabola, then k in

Parabolas (y-alpha)^(2)=4a(x-beta)and(y-alpha)^(2)=4a'(x-beta') will have a common normal (other than the normal passing through vertex of parabola) if

If a,b,c are distincl positive real numbers such that the parabola y^(2) = 4ax and y^(2) = 4c ( x - b) will have a common normal, then prove that (b)/(a-c) gt 2

Prove that If any A B C are distinct positive numbers , then the expression (b+c-a)(c+a-b)(a+b-c)-abc is negative