Let `A` and `B` two drawing pins,`AB=10` and let `a` string whose ends at `A ,B` and length is `16` .The point of pencil moves on paper and fixed ends always tight.We get a curve on paper its area is`

Imagine that you have two thumbtacks placed at two points, A and B. If the ends of a fixed length of string are fastened to the thumtacks and the string is drawn taut with a pencil, the path traced by the pencil will be an ellipse. The best way to maximise the area surrounded by the ellipse with a fixed length of string occurs I when the two points A and B have the maximum distance between them. II two points A and B coincide.IIIA and B are placed vertically.IV The area is always same regardless of the location of A and B.

Let A and B be two points on y^(2)=4ax such that normals to the curve at A and B meet at point C, on the curve, then chord AB will always pass through a fixed point whose coordinates, are

Let A(0,-4) and B(0,4) be two fixed points. Find the locus of a point P which moves so that PA+PB=12 .

A thin pencil of mass M and length L is being moved in a plane so that its centre (i.e. centre of mass) goes in a circular path of radius R at a constant angular speed omega . However, the orientation of the pencil does not change in space. Its tip (A) always remains above the other end (B) in the figure shown (a) Write the kinetic energy of the pencil. (b) Find the magnitude of net force acting on the pencil.

A rod AB of length 15cm rests in between two coordinate axes in such a way that the end point A lies on x- axis and end point B lies on y -axis.A point is taken on the rod in such a way that AP=6cm. Show that the locus of P is an ellipse.Also find its eccentricity.

A particle is moving in a circular path in the vertical plane. It is attached at one end of a string of length l whose other end is fixed. The velocity at lowest point is u . The tension in the string T and acceleration of the partiocle is a any position. Then T a is zero at highest point if

Let O be the origin and A, B be the two points having coordinates (0, 4) and (6, 0) respectively. If a point P moves in such a way that the area of the Delta OPA is always twice the area of Delta POB , then P lies on

A string of linear mass density 0.5 g cm^-1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end. The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s^-1 . The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape. (b) The shape of the string changes periodically with time. Find this time period. (c) What is the tension in the string ?