If graphs of `y = ax - b & y = x^2 + (3a - 1)x + a^2` touch each other, where `a,b in R`, then `a + b` is equal to-

If circles x^(2) + y^(2) = 9 " and " x^(2) + y^(2) + 2ax + 2y + 1 = 0 touch each other , then a =

Let parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0) then b-c=

If the parabolas y=x^(2)+ax+b and y=x(c-x) touch each other at the point (1,0), then a+b+c=

Let the parabolas y= x^(2)+ ax +b and y =x(c-x) touch cach other at point (1,0). Then

The curves y=x^(2)+x+1 and 2y=x^(3)+5x touch each other at the point

The curves y=x^(3)+x+1 and 2y=x^(3)+5x touch each other at the point

Let the parabolas y=x(c-x)and y=x^(2)+ax+b touch each other at the point (1,0), then-

Let the parabolas y=x(c-x)and y=x^(2)+ax+b touch each other at the point (1,0), then-

If the circles x ^2 + y ^2 + 2ax + c = 0 and x ^2 + y ^2 +2by + c = 0 touch each other, prove that 1/a ^2 + 1 b ^2 = 1/c