Analytic Geometry Answers

what surface is represented by x^2 + y^2 = 9z ? Give a rough sketch of it. Obtain the section
of this surface by the plane y = 0.

Find the equations of the straight lines which pass through the intersection of 3x-4y+1=0 and 5x+y=1 and which cut off equal intercepts from the axes

Prove that if ABC is triangle and Dis the mid point of BC , then AB^2+AC^2,=2*AD^2+DC^2)

If (-3,4) lies on a curve that is symmetric with respect to the x-axis ,then (3,4) will also lie on the curve.

A car travels 3km due north, then 5km northeast. Determine the resultant displacement

a) Find the equation of the sphere which passes through the points
(1, − 4, 3), (1, − 5, 2), (1, − 3, 0) and whose centre lies on the plane x + y + z = 0 .

find the projection of the vectr i-j (cap) on the vector i+j (cap)?

What is the radius of the circle if the center of the circle is C(-3,5) and the point P(5,11) is on the circle?

Find an equation of each normal line to the curve: y = x^3 - 4x that is parallel to the line
x + 8y - 8 = 0

gent to the the line 4x-3y=6 at (3,2) and passing through (2,-1)