A man running a racecourse notes that the sum of the distances from the two flag posts from him is always `10` m and the distance between the flag posts is `8` m. Find the equation of the posts traced by the man.

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c^2dot Find the equation to its locus.

Two poles of heights 6 m and 11m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

Two poles of heights 6m and 11m stand on a plane ground. If the distance between the feet of the poles is 12m find the distance between their tops.

Find the equation of the set of al points the sum of whose distance from the points (3,0) and (9,0) is 12.

The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is 60^(@) and the angle of elevation of the top the second tower from the foot of the first tower is 30^(@) . Find the distance between the two towers and also find the height of the other tower.

IF the distribution of weight is uniform, then the rope of the suspended bridge takes the form of parabola.The height of the supporting towers is 20m, the distance between these towers is 150m and the height of the lowest point of the rope from the road is 3m. Find the equation of the parabolic shape of the rope considering the floor of the parabolic shape of the rope considering the floor of the bridge as X-axis and the axis of the parabola as Y-axis. Find the height of that tower which supports the rope and is at a distance of 30 m from the centre of the road.

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the given figure. Niharika runs (1)/(4) th the distance AD on the 2nd line and posts a green flag. Preet runs (1)/(5) th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags ? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag ?

A person 1.65m tall casts 1.8m shadow. At the same instance, a lamp post casts a shadow of 5.4 m. Find the height of the lamppost.

In Young's experiment, the distance between two slits is 1 mm and the distance between two consecutive bright fringes is 0.03 cm. Now, on displacing the screen away from the slits by 50 cm, the distance between two consecutive dark fringes is doubled. Find the wavelength of light used.

Distance of two planets from the sun are 10^11 m and 10^(10) m respectively. Then find the ratio of time period of these two planets.