Question

Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,  

                                

Solution

Correct option is

Here,                            

When parametric coordinates are given by;   

                       

  

  

⇒ Equation of tangent,

                         

∴ x-intercept,   

  

and y-intercept;   

  

Hence, the sum of intercept made on the axes of coordinates is,  

                             

SIMILAR QUESTIONS

Q1

If the displacement of a particle is given by  Find the velocity and acceleration at t = 4 second.

Q2

x and y are the sides of two squares such that y = x – x2. Find the rate of change of the area of the second square with respect to the first square.

Q3

Find equation of tangent to the curve 2y = x2 + 3 at (x1y1).

Q4

Find the equation of tangent to the curve y2 = 4ax at (at2, 2at).

Q5

The tangent represented by the graph of the function y = (x) at the point with abscissa x = 1 form an angle π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle π/4. Then find the value of,  

                                                

Q6

Three normals are drawn from the point (c, 0) to the curve y2 = x, show that c must be greater than ½. One normal is always the x-axis. Find c for which the other normals are perpendicular to each other.

Q7

Find the acute angle between the curves y = | x2 – 1| and y = | x2 – 3 | at their points of intersection when x > 0.

Q8

If the relation between subnormal SN and subtangent ST at any point S on the curve; by2 = (x + a)3 is p(SN) = q(ST)2, then find the value of p/q. 

Q9

 in which interval

Q10

If f (x) = xα log x and f (0) = 0, then the value of ‘α’ for which Rolle’s theorem can be applied in [0, 1] is: