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Analytic Geometry
Find the principal axis, vertex, focus, directrix, endpoints of the focal width and length of the focal width, and sketch the graph of the following:
1. -(x + 5)^2 = y
2. (y - 8)^2 = 24(x + 1)
3. 4x - y^2 = 0
1. -(x + 5)^2 = y
2. (y - 8)^2 = 24(x + 1)
3. 4x - y^2 = 0
Analytic Geometry
Find the equation to the straight line passing through the point of intersection of the lines 5x–6y –1 = 0 and 3x + 2y +5 =0 and perpendicular to the line 3x–5y+11 = 0
Analytic Geometry
Find the equation of the sphere which passes through the points 0)3,(1,2),5,(1,3),4,(1, −−− and whose centre lies on the plane 0 =++ yzx .
Analytic Geometry
A = sin ti + cos tj + tk, evaluate
d2A/dt2
d2A/dt2
Analytic Geometry
Find the radius and the center of the circular section of the sphere |r| = 4 cut off by the
plane r·(2i−j+ 4k) = 3
plane r·(2i−j+ 4k) = 3
Analytic Geometry
A straight line slides along the axes (oblique) of x and y, and the difference of the intercepts is
always proportional to the area it encloses. Show that the line always passes through a fixed point
always proportional to the area it encloses. Show that the line always passes through a fixed point
Analytic Geometry
Derive the equation of the right circular cone generated by rotating the line 6x=3y=2z about the line 2x=-2y=-z
Analytic Geometry
Vectors intersection question:
A line can either lie on a plane, lie parallel to it or intersect it.
Determine, if there is one, the point of intersection between the line given by the equation:
x-5/2= y-1/-1 = z-15/4 and the plane given by the equation:
[x,y,z]= [-2,-7,5]+ s[2,6,3]+ t[1,4,-1]
b)Determine the angle between the line and the plane.
c)Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane.
A line can either lie on a plane, lie parallel to it or intersect it.
Determine, if there is one, the point of intersection between the line given by the equation:
x-5/2= y-1/-1 = z-15/4 and the plane given by the equation:
[x,y,z]= [-2,-7,5]+ s[2,6,3]+ t[1,4,-1]
b)Determine the angle between the line and the plane.
c)Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane.
Analytic Geometry
A third plane can be found that passes through the line of intersection of two existing planes.?
a. Two planes are given by the equations 2x − 3y + z − 6 = 0 and -3x + 5y + 4z + 6 = 0. Find the scalar equation of the plane that passes through the line of intersection of these two planes, and also passes through the point (1, 3, -1).
b. Give the equations of two planes. Create a third plane that passes through the line of intersection of the original two and which is parallel to the z-axis. Explain your reasoning
a. Two planes are given by the equations 2x − 3y + z − 6 = 0 and -3x + 5y + 4z + 6 = 0. Find the scalar equation of the plane that passes through the line of intersection of these two planes, and also passes through the point (1, 3, -1).
b. Give the equations of two planes. Create a third plane that passes through the line of intersection of the original two and which is parallel to the z-axis. Explain your reasoning
Analytic Geometry
Triangle ABC has vertices A(-1, 1, 3), B(-1, 3, 5), and C(-3, 3, 3). What kind of triangle is ΔABC? Justify your answer
