Angle of intersection of the curves y=4-x^2 and y=x^2 is (a) (π)/(2) (b) tan^-1((4)/(3)) (c) tan

step 1 In this question, we are given two curves, y is equal to 4 minus x squared and y is equal to x s

Angle of intersection of the curves y=4-x^2 and y=x^2 is (a)...

Key Concepts

Inverse Tangent Function

Also known as arctan, the inverse tangent function is used to determine an angle given the ratio of the opposite to the adjacent side in a right triangle. It is essential in converting the computed tangent (slope ratio) of the angle between curves into the actual angle measure.

Derivative

In calculus, the derivative of a function at a particular point represents the slope of the tangent line to the curve at that point. It quantifies the rate at which the function value changes with respect to changes in the independent variable.

Angle Between Tangent Lines

The angle of intersection between two curves is defined as the angle between their tangent lines at the point of intersection. This angle can be calculated using a formula that involves the slopes of the tangent lines, making it a critical bridge between calculus and geometry.

Intersection of Curves

This concept refers to the points where two curves meet. At such points, the curves share common coordinates, and determining these points is fundamental before analyzing any geometric properties, such as the angles at which the curves intersect.

Tangent Lines

A tangent line to a curve at a given point is the straight line that best approximates the curve near that point. The behavior of a curve near an intersection is often analyzed by considering the tangent lines at the intersection point.

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