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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
Find the new equation of the conicoid 184x^2 - 236xy + 88xz + 169y^2 - 14yz + 88z^2 =324 when the coordinate system xyz is transformed into another coordinate system x'y'z' under the transformations given by the following table:
x y z
x' 2/3 -2/3 1/3
y' 1/3 2/3 2/3
z' -2/3 -1/3 2/3
What object does this new equation represents in the coordinates system x'y'z' ?
Does the old equation represent the same object in the coordinate system xyz ?
Justify your answer.
x y z
x' 2/3 -2/3 1/3
y' 1/3 2/3 2/3
z' -2/3 -1/3 2/3
What object does this new equation represents in the coordinates system x'y'z' ?
Does the old equation represent the same object in the coordinate system xyz ?
Justify your answer.
Analytic Geometry
Find the angle between the lines x = 1 , z - y = 0 and 2x - y = -1 , z = 1 .
Analytic Geometry
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.
x/y = y/(-1) = z/2 and 2x = y , y-z = 0.
Analytic Geometry
r a circle described on any focal chord of the parabola y2=4ax as its diameter will touch which part of parabola?
Analytic Geometry
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.
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.
Analytic Geometry
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
Analytic Geometry
Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.
Analytic Geometry
Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.
Analytic Geometry
Find the rectangular coordinates of the point with the polar coordinates (8, 3 divided by 2 pi).
