Question

Find the acute angle between the curves 

 at their points of intersection when x > 0.

Solution

Correct option is

For the intersection of the given curves

                  

   

  

  

   

   

                

we have point of intersection as    

  

In the neighbouring of  and     

                     

in the neighbouring of   

Hence, if θ is angle between them,   

  

  

SIMILAR QUESTIONS

Q1

The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x2 – x | is

Q2

The tangent to the graph of the function y = f (x) at the point with abscissax = 1 form an angle of π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle of π/4. The value of 

                          

Q3

The equations of the tangents to the curve y = x4 from the point (2, 0) not on the curve, are given by

Q4

The value of parameter a so that line (3 – ax + ay + (a2n – 1) = 0 is normal to the curve xy = 1, may lie in the interval

Q5

A cylindrical gas container is closed at the top and open at the bottom; if the iron plate forming the cylindrical sides. The ratio of the height to diameter of the diameter of the cylindrical using minimum material for the same capacity is

Q6

The critical points of the function f (x) where 

Q7

Find the abscissa of the point on the curve ay2 = x3, the normal at which cuts of equal intercept from the axes.

Q8

Find the condition that the curves; ax2 + by2 = 1 and a ‘x2 + b’ y2 = 1 may cut each other orthogonally (at right angles).

Q9

Find the locus of a point that divides a chord of slope 2 of the parabola y2= 4x internally in the ratio 1: 2.