The given bends are
![\[y\text{ }=\text{ }4\text{ }\text{ }x2\text{ }\ldots \text{ }.\text{ }\left( I \right)\text{ }and\text{ }y\text{ }=\text{ }x2\text{ }\ldots \text{ }\left( ii \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-62f7c070f6af0a4259b86880ac93ca29_l3.png "Rendered by QuickLaTeX.com")
Also, we realize that the point of convergence of two bends is equivalent to the point between the digressions attracted to the bends at their place of convergence.
Presently, separating conditions (I) and (ii) w.r.t x, we have
![\[dy/dx\text{ }=\text{ }-\text{ }2x\Rightarrow m1\text{ }=\text{ }-\text{ }2x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3a297588338395005e0bda695fa95310_l3.png "Rendered by QuickLaTeX.com")
m1 is the incline of the digression to the bend (I).
also,
![\[dy/dx\text{ }=\text{ }2x\Rightarrow m2\text{ }=\text{ }2x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c88df52e43dfcb8bb675fb3d30b9fe6_l3.png "Rendered by QuickLaTeX.com")
m2 is the incline of the digression to the bend (ii).
Thus,
![\[m1\text{ }=\text{ }-\text{ }2x\text{ }and\text{ }m2\text{ }=\text{ }2x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7ccba228e52914aea1710c43624cef56_l3.png "Rendered by QuickLaTeX.com")
On tackling condition (I) and (ii), we get
![\[4\text{ }\text{ }x2\text{ }=\text{ }x2\Rightarrow 2x2\text{ }=\text{ }4\Rightarrow x2\text{ }=\text{ }2\Rightarrow x\text{ }=\text{ }\pm \surd 2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c18523193118bd2b076c36433865d09a_l3.png "Rendered by QuickLaTeX.com")
Thus,
![\[m1\text{ }=\text{ }-\text{ }2x\text{ }=\text{ }-\text{ }2\surd 2\text{ }and\text{ }m2\text{ }=\text{ }2x\text{ }=\text{ }2\surd 2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cb35cfb7c7acb1f3460e5069427b36ac_l3.png "Rendered by QuickLaTeX.com")
Let θ be the point of convergence of two bends
