A line segment moves in the plane
with its end points on the coordinate
axes so that the sum of the length
of its intersect on the coordinate
axes is a constant C .
Find the locus of the mid points of
this segment .
Ans. is 8(∣x∣^3 +∣y∣^3 )=C .
Λ means power . pls. solve it.
A string is stretched and fastened to two points l apart. Motion is started
by displacing the string into the form y = (lx − x^2 ) from which it is release
at time t = 0. Find the displacement of any point on the spring at a distance
x from one end at time t.
The triangle ABC has CA = CB. P is a
point on the circumcircle between A
and B (and on the opposite side of the
line AB to C). D is the foot of the
perpendicular from C to PB. Show that
PA + PB = 2∙PD.
The accompanying diagram is a road-
plan of a city. All the roads go east-
west or north-south, with the
exception of one shown. Due to repairs
one road is impassable at the point X,
Of all the possible routes from P to Q,
there are several shortest routes. How
many such shortest routes are there?
A train, after travelling 70 km from a
station A towards a station B, develops
a fault in the engine at C, and covers
the remaining journey to B at (3/4) of its
earlier speed and arrives at B 1 hour
and 20 minutes late. If the fault had
developed 35 km further on at D, it
would have arrived 20 minutes sooner.
Find the speed of the train and the
distance from A to B.
a particle starts with an initial
speed u,it moves in a straight
line with an accleration which
varies as the square of the time
the particle has been in motion.
Find the speed at any time t,and
the distance travelled.
The circle ω touches the circle Ω
internally at P. The centre O of Ω is
outside ω. Let XY be a diameter of Ω
which is also tangent to ω. Assume
PY > PX. Let PY intersect ω at Z. If
YZ = 2PZ, what is the magnitude of
∠PYX in degrees?