Advertisements
Advertisements
प्रश्न
Find the positive value of m for which the distance between the points A(5, −3) and B(13, m) is 10 units.
उत्तर
It is given that distance between A(5, −3) and B(13, m) is 10 units.
⇒ `"AB" = sqrt((5-13)^2 +(-3-"m")^2)`
⇒ `10 = sqrt(64+9+6"m"+"m"^2)`
⇒ 100 = 73 + 6m +m2
⇒ m2 + 6m - 27 = 0
⇒ m2 +9m - 3m - 27 =0
⇒ m (m+9) - 3 (m-9)=0
⇒ (m-3) (m+9) =0
⇒ m=3, -9
Hence, the positive value of m is 3.
APPEARS IN
संबंधित प्रश्न
The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 300 If the aeroplane is flying at a constant height of 3000 3 m, find the speed of the aeroplane.
The pilot of a helicopter, at an altitude of 1200m finds that the two ships are sailing towards it in the same direction. The angle of depression of the ships as observed from the helicopter are 60º and 45º respectively. Find the distance between the two ships
The angles of elevation of the top of a tower from two points at distance of 5 metres and 20 metres from the base of the tower and is the same straight line with it, are complementary. Find the height of the tower.
The angle of elevation of the top of a vertical tower from a point on the ground is 60° . From another point 10 m vertically above the first, its angle of elevation is 30° .Find the height of the tower.
If the angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
A ladder makes an angle of 60º with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building.
Two towers A and B are standing some distance apart. From the top of tower A, the angle of depression of the foot of tower B is found to be 30°. From the top of tower B, the angle of depression of the foot of tower A is found to be 60°. If the height of tower B is ‘h’ m then the height of tower A in terms of ‘h’ is ____________ m.
A window of a house is h meters above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be A and B respectively. Then the height of the other house is ____________.
Two circles of radii 5 cm and 3 cm touch each other externally. Find the distance between their centres.
