Find the sum of the intercepts on the axes of coordinates by any tangent to the curve,
When parametric coordinates are given by;
⇒ Equation of tangent,
Hence, the sum of intercept made on the axes of coordinates is,
If the displacement of a particle is given by Find the velocity and acceleration at t = 4 second.
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.
Find equation of tangent to the curve 2y = x2 + 3 at (x1, y1).
Find the equation of tangent to the curve y2 = 4ax at (at2, 2at).
The tangent represented by the graph of the function y = f (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,
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.
Find the acute angle between the curves y = | x2 – 1| and y = | x2 – 3 | at their points of intersection when x > 0.
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.
in which interval
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: