Example 5

Prove that the curves y² = 16x and 2x² + y² = 4 cut each other orthogonally.

Solution : Let P (x₁, y₁) be a point of intersection of the curves

y² = 16x ... (1) and

2x² + y² = 4 ... (2)

\ = 16x1 ... (3) and

Let m₁ and m₂ be the two slopes of the two tangents to the curve (1) and (2) at P respectively.

By Differentiating w. r. to x , the equation (1), we get

[next page]

Index

5.1 Tangent And Normal Lines
5.2 Angle Between Two Curves
5.3 Interpretation Of The Sign Of The Derivative
5.4 Locality Increasing Or Decreasing Functions 5.5 Critical Points
5.6 Turning Points
5.7 Extreme Value Theorem
5.8 The Mean-value Theorem
5.9 First Derivative Test For Local Extrema
5.10 Second Derivative Test For Local Extrema
5.11 Stationary Points
5.12 Concavity And Points Of Inflection
5.13 Rate Measure (distance, Velocity And Acceleration)
5.14 Related Rates
5.15 Differentials : Errors And Approximation

Chapter 6