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Analytic Geometry
Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3.
Analytic Geometry
Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.
Analytic Geometry
Trace the conicoid given by x^2 + 2z^2 = 4y. What are the sections of this
conicoid by the planes x+2=0 and y=1 ?
Describe geometrically.
conicoid by the planes x+2=0 and y=1 ?
Describe geometrically.
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 new equation of the conicoid 9x^2 + 16y^2 - 36z^2 - 36x - 72z = 144 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.
Analytic Geometry
At what point the origin must be shifted so that linear terms in the conicoid x^2 + 2y^2 - z^2 - 2yz + 2xz + x - 3y + z + 4 = 0 vanish? Justify.
Analytic Geometry
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).
Analytic Geometry
Show that the angle between the two lines in which the plane x - y + 2z = 0 intersects the cone x^2 + y^2 - 4z^2 + 6yz = 0 is tan inverse of (under-root 6 / 7) .
Analytic Geometry
Find the centre and radius of the circle x^2 + y^2 + z^2 + 2x + 2y + 4z = 3, 2x - y - z = 3.
Analytic Geometry
Under what conditions on (alpha) , the spheres x^2 + y^2 + z^2 + (alpha)x - y = 0 and x^2 + Y^2 + z^2 + x +2z +1 = 0 intersect each other at an angle of 45^0.
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#332078 on Oct 2022
#332078 on Oct 2022