Analytic Geometry Answers

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 .

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)

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.

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 .

Find the angle between the lines x = 1 , z - y = 0 and 2x - y = -1 , z = 1 .

Find the path traced by the centre of the sphere which touches the lines
x/y = y/(-1) = z/2 and 2x = y , y-z = 0.

r a circle described on any focal chord of the parabola y2=4ax as its diameter will touch which part of parabola?

An elliptical riding path is to be built on a rectangular piece of property as shown below.

The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1

Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.