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Analytic Geometry
Find the distance of the line obtained in part (a), from the origin by expressing it in the normal form. Also find the intercepts made by this line on the coordinate axes.
Analytic Geometry
Find the equation of the pline which passes through (1,root3) and makes an angle 30 with the line x-root3y+root3=0
Analytic Geometry
Find the equation of the plane which passes through the line of intersection of the planes 2x+y-2z=6 and makes equal angles with 2x+3y+6z=5 these planes.
Analytic Geometry
Find the angle between the lines x=1 z-y=0 and 2x-y=-1,z=1
Analytic Geometry
For what value(s) of α, the conicoid x^2+y^2+az^2+2yz +xy+2y+z+3=0 has a unique centre? Give reason for your answer.
Analytic Geometry
Find the equation of the cylinder with base curve x^2+y^2+z^2-2x-4z+1=0,2X+y+z=2
Analytic Geometry
Find the path traced by the centre of the sphere which touches the lines x/y=y/-1z/2
and 2x=y,y-z=0 .
and 2x=y,y-z=0 .
Analytic Geometry
If
,
1
x f
x
x
show that
. 0 1
"
f
(3)
(b) Find the n
th
derivative of
.
2 2
a x
x
(3)
(c) If cos
,
n
x
log
b
y
n
then show that
0 2 1 2
2
1 2
2
n n n y n xy n y x
(4)
,
1
x f
x
x
show that
. 0 1
"
f
(3)
(b) Find the n
th
derivative of
.
2 2
a x
x
(3)
(c) If cos
,
n
x
log
b
y
n
then show that
0 2 1 2
2
1 2
2
n n n y n xy n y x
(4)
Analytic Geometry
Find the new equation of the conicoid
when the coordinate system is changed into a new system with the same origin at
(-2, 0, 1) and direction ratios same as the old system. (4)
(b) Find the new equation of the conicoid
when the coordinate system is transformed into another
coordinate system under the transformations given by the following table:
What object does this new equation represents in the coordinates system ?
Does the old equation represent the same object in the coordinate system ?
Justify your answer. (6)
(c) Trace the conicoid given by What are the sections of this
conicoid by the planes and Describe geometrically.
when the coordinate system is changed into a new system with the same origin at
(-2, 0, 1) and direction ratios same as the old system. (4)
(b) Find the new equation of the conicoid
when the coordinate system is transformed into another
coordinate system under the transformations given by the following table:
What object does this new equation represents in the coordinates system ?
Does the old equation represent the same object in the coordinate system ?
Justify your answer. (6)
(c) Trace the conicoid given by What are the sections of this
conicoid by the planes and Describe geometrically.
Analytic Geometry
Show that the angle between the two lines in which the plane
intersects the cone is . (4)
(b) Using projection show that the line passing through (-1, 8, 8) and (6, 2, 0) is
perpendicular to the line passing through (4, 2, 3) and (2, 1, 2). (2)
(c) At what point the origin must be shifted so that linear terms in the conicoid
vanish? Justify.
intersects the cone is . (4)
(b) Using projection show that the line passing through (-1, 8, 8) and (6, 2, 0) is
perpendicular to the line passing through (4, 2, 3) and (2, 1, 2). (2)
(c) At what point the origin must be shifted so that linear terms in the conicoid
vanish? Justify.
