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Home » Find the angle of intersection of the curves y = 4 – x2 and y = x2.
Find the angle of intersection of the curves y = 4 – x2 and y = x2.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Find the angle of intersection of the curves y = 4 – x2 and y = x2.

The given bends are

    \[y\text{ }=\text{ }4\text{ }\text{ }x2\text{ }\ldots \text{ }.\text{ }\left( I \right)\text{ }and\text{ }y\text{ }=\text{ }x2\text{ }\ldots \text{ }\left( ii \right)\]

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

 

    \[dy/dx\text{ }=\text{ }-\text{ }2x\Rightarrow m1\text{ }=\text{ }-\text{ }2x\]

m1 is the incline of the digression to the bend (I).

also,

    \[dy/dx\text{ }=\text{ }2x\Rightarrow m2\text{ }=\text{ }2x\]

m2 is the incline of the digression to the bend (ii).

Thus,

    \[m1\text{ }=\text{ }-\text{ }2x\text{ }and\text{ }m2\text{ }=\text{ }2x\]

On tackling condition (I) and (ii), we get

    \[4\text{ }\text{ }x2\text{ }=\text{ }x2\Rightarrow 2x2\text{ }=\text{ }4\Rightarrow x2\text{ }=\text{ }2\Rightarrow x\text{ }=\text{ }\pm \surd 2\]

Thus,

    \[m1\text{ }=\text{ }-\text{ }2x\text{ }=\text{ }-\text{ }2\surd 2\text{ }and\text{ }m2\text{ }=\text{ }2x\text{ }=\text{ }2\surd 2\]

Let θ be the point of convergence of two bends

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 23

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