Answer :

Given: the curves y = 4–x2 and y = x2


To find: the angle of intersection of the two curves


Explanation: consider first curve


y = 4–x2


Differentiating the above curve with respect to x we get




Consider second curve


y = x2


Differentiating the above curve with respect to x we get




Given y = x2


Substituting this in other curve equation, we get


x2 = 4-x2


2x2 = 4


x2 = 2


x = ±√2


When x = √2, we get


y = (√2)2 y = 2


When x = -√2, we get


y = (-√2)2 y = 2


Thus the points of intersection are (√2, 2) and (-√2, 2)


We know angle of intersection can be found by following formula,


i.e.,


Substituting the values from equation (i) and equation (ii), we get




For (√2, 2), the above equation becomes,





Hence the angle of intersection of the curves y = 4–x2 and y = x2 is


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