a parabola y=x^2 −15x+36 cuts the
x axis at P and Q. a circle is drawn
through P and Q so that the origin
is outside it. then find the length
of tangent to the circle from (0,0)?
Solid cube ABCD.EFGH is cut by a
plane X so that it forms a plane of slices
IJKLMN where I is mid AB, J is mid BF
K is mid FG, L is mid HG, M mid DH
and N mid AD. If the edge of the cube
is X, find the area of the IJKLMN field
Cube ABCD.EFGH has side length a.
Point P lies on AC such that AP : PC = 3 : 1 Through P a line l parallel to BD is
drawn such that l each intersect BC at
X and CD at Y. If AC and BD
intersect at O find the distance
between XY with OG!
There are two circles , C of radius 1 and C_r
of radius r which intersect on a plain
At each of the two intersecting
points on the circumferences of
C and C_r ,the tangent to C and
that to C_r form an angle 120° outside
of C and C_r . Fill in the blanks
with the answers to the following
questions
(1) Express the distance d between
the centers of C and C_r in terms
of r
(2) Calculate the value of r at
which d in (1) attains the minimum
(3) in case(2) express the area
of the intersection of C and C_r
in terms of the constant π
consider the circle
(x−1)^2 +(y−1)^2 =2,
A(1,4), B(1,−5). if P is
a point on the circle such that
PA+PB is maximum then
prove that P,A,B are collinear
points.