Question

assume that the normal lines at each point of a surface passes through the same fixed point. Show that this surface x(u,v) is a part of a sphere

Answer #1

Three parallel lines are such that one passes through each
vertex of a triangle ABC, and they are not parallel to any of the
triangles sides. The line through A meets BC (extended if
necessary) in X, the lines through B and C meet CA and AB in Y and
Z respectively. Prove that area(XYZ) = 2xArea(ABC)

A
tangent to a circle at the point (5,5) passes through the origin.
The line with equation 3y=x+2 is a normal to the circle.
(i) Show all working, find the equation of the circle.
(ii) Find the coordinates of the point on the circle whih is
nearest to the x-axis.

At which point the normal line that passes through the point (1,
-1,1) on the ellipsoid 2x2 + y2 + 2z2 = 5 crosses the xy coordinate
plane

A cord is attached to the ceiling at a fixed point and passes
through an eye screw 10 meters beyond. On the string, 5 meters from
the fixed point, a box is attached. the box is so heavy that the
string becomes a straight line both from the fixed point to the box
and from the box to the eye screw.
You pull the cord (through the eye screw) at a speed of 1 meter per
second. At a time...

The planar surface passes through three point (2,0,2), (2,1,2),
(1,2,0). Determine the cartesian equation for the surface and find
the shortest distance between the body and the surface given that
the body lies at (1,1,5).

Find an equation of the sphere determined by the given
information.
passes through the point (6, 3, -5), center (5, 8, 1)

Find vector and parametric equations for:
a) the line that passes through the point P(9,-9,6) parallel to
the vector u = <3,4,-2>
b) the line passing through the point P(6,-2,6) parallel to the
line x=2t, y = 2 - 3t, z = 3 +6t
c) the line passing through the point P(5, -2,1) parallel to the
line x = 3 - t, y = -2 +4t, z = 4 + 8t

What is the equation of the curve that passes through the point
(0,6)and at every point P on the curve its slope is three times the
y-coordinate of P?
y(x)=?

What are the equations of the tangent and normal lines to the
following curve: y2+y+x =
arctan2(sin3(x)) at point (0,-1) Remember
that (arctan (u)=tan-1(u))

What is the equation of the line which passes through the point
( x 0 , y 0 ) = ( 1 , 4 )with slope m = 5?

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