Analytic Geometry Answers

Trace the conicoid represented by x^2 +2z^2 = y. Also describe its sections by the planes x = c,∀c ∈ R.

Find the nature of the planar section of the conicoid x^2÷3 −y^2÷4 = z by the plane

x+2y−z = 6

Find the equation of the cone with the vertex at (1,−1,2) and the base curve as

(z+1)^2 = x+2, y = 3.

Show that x = y = z+1 is a secant line of the sphere x^2 +y^2 +z^2 −x−y+z−1 = 0.

Also find the intercept made by the sphere on the line.

Consider two lines L1 and L2 whose direction cosines l1,m1,n1 and l2,m2,n2 are given by the equations for l,m,n :

al +bm+cn = 0, fmn+gnl +hlm = 0,

where abc is not equal to 0. Show that if L1 ⊥ L2, then f÷a + g÷b + h÷c = 0.

How many lines on the coordinate plane that has a distance 1 to the origin O(0,0) and distance 2 to the point A (3,0)?

Vectors of points A and B are 2i-3j+4k and 3i-7j+12k respectively

Find the vector equation of the plane determined by the points (1, 0, −1),

(0, 1, 1) and (−1, 1, 0). Also nd the point of intersection of the line

Determine the equation of line of distance P from the origin

the equations [1,2] + t[3,2] and [7,6] + t[-6,-4] give the same line, as(7,6) is a point on the first line,and the direction vectors are scalar multiples of each other. give a third equation that generates the same line.write another two different ewuations that give the same line as each other. include a langraph of your lines