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

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10m 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^2 . Find the equation to its locus.

A beam of ligth consisting of two wavelength 4,800 overset@A and 6,000 overset@A is used to obtain interfernce fringes in a double slit experiment.The distnce between the slits is 1.8 mm and the distance of screen from the plane of slits is 1.2 m Find the distance of the third bright frings on the screen from the central maximum for the wavelength 6,000 overset @A .

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.

A beam of ligth consisting of two wavelength 4,800 overset@A and 6,000 overset@A is used to obtain interfernce fringes in a double slit experiment.The distnce between the slits is 1.8 mm and the distance of screen from the plane of slits is 1.2 m What is the lest distance from the centre of the screen,where the brigth fringes due to both the wvelength coincide?

The radius of curvature of a railway line at a place is 40000m.the train is running at 20 m s^-1 .the distance between the two rails is 1.5 m.Find the elevation of the outer rail over the inner one so that the train may be able to run safely.

In Young's double slit experiment the width of the fringes obtained with ith of wavelength 4,500 overset@A is 1.8 mm.If the distance between the two slits is 0.3 mm,find the distance of the screen from the slits.What will be the fringe width,if the enitre apparatus is immersed in water of refraction index 4//3 .

From a building 60 metres high the angle of depression of the top and bottom of lamppost are 30^@ and 60^@ respectively. Find the distance between lamp post and building. Also find the difference of height between building and lamp post.

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 1m from each other along AD, as shown in Fig. 7. 12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th 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?

From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30^@ .A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45^@ . Find the length of the flagstaff and the distance of the building from the point P. (You may take sqrt3 = 1.732)