Given bend conditions are: \[y2\text{ }=\text{ }4x\text{ }\ldots \text{ }.\text{ }\left( 1 \right)\text{ }and\text{ }x2\text{ }+\text{ }y2\text{ }\text{ }6x\text{ }+\text{ }1\text{ }=\text{ }0\text{ }\ldots \text{ }..\text{ }\left( 2 \right)\]

Presently, separating (I) w.r.t. x, we get

\[2y.\left( dy/dx \right)\text{ }=\text{ }4\Rightarrow dy/dx\text{ }=\text{ }2/y\]

Slant of digression at (1, 2), \[m1\text{ }=\text{ }2/2\text{ }=\text{ }1\]

Separating (ii) w.r.t. x, we get

\[2x\text{ }+\text{ }2y.\left( dy/dx \right)\text{ }\text{ }6\text{ }=\text{ }0\]

\[2y.\text{ }dy/dx\text{ }=\text{ }6\text{ }\text{ }2x\Rightarrow dy/dx\text{ }=\text{ }\left( 6\text{ }\text{ }2x \right)/2y\]

Subsequently, the incline of the digression at a similar point (1, 2)

\[\Rightarrow m2\text{ }=\text{ }\left( 6\text{ }\text{ }2\text{ }x\text{ }1 \right)/\left( 2\text{ }x\text{ }2 \right)\text{ }=\text{ }4/4\text{ }=\text{ }1\]

It’s seen that \[m1\text{ }=\text{ }m2\text{ }=\text{ }1\] at the point \[\left( 1,\text{ }2 \right).\]

Subsequently, the given circles contact each other at a similar point \[\left( 1,\text{ }2 \right).\]