A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so ? If yes, at what distances from the two gates should the pole be erected ?

The locus of a point which moves so that the difference of the squares of its distance from two given points is constant, is a

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60^@ and 30^@ , respectively. Find the height of the poles and the distances of the point from the poles.

The moon is observed from two points P and Q on the earth which are diametrically opposite. The angle subtended at moon by two directions of observation is 1@(54)' . The diameter of earth is 1.27xx10^(7)m . Calcualte the distance of moon from the earth.

Draw a circle of radius 3cm. Take two point P and Q on one of its extended diameter each at distance of 7cm from its centre. Draw tangents to the circle from these two points P and Q

The principle of 'parallax' is used in the determination of distance of nearby stars. The role of distant object O there is now taken by nearby distant stars. The baseline AB is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is the baseline is about the disameter of the earth's orbit = 3 xx 10^11 m. However, even the nearest stars are so distant that with such a long baseline theyshow parallax only of the order 1 s of arc or so. A parsec is a convenient unit of length on the astronomical sxale. It is the distance of an object that will show a parallar of 1s of arc from opposite ends of a baseline equal to the distance from the Earth to the Sum How much is a parsec in terms of metre?

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?

Two fixed, equal, positive charges, each of magnitude 5xx10^-5 coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB. The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.