Analytic Geometry Answers

find the equation of the normal to the parabola y^2+4x=0 at the point where the line y=x+c touches it

Find the equation of the tangent plane to the conicoid x^2+y^2 = kz at the point
(k;k;2k), where k is a constant. Represent the plane geometrically. Now take
different values of k, including both positive and negative, and see how the shape of
the conicoid changes.

Identify and trace the conicoid y^2+z^2 = x. Describe its sections by the planes
x = 0;y = 0 and z = 0.

Find the vertices, eccentricity, foci and asymptotes of the hyperbola x2
8

Equation of one side of a square is 2x+3y+4=0. If the center is (1,1) then find the equations of adjoined two sides of the square.

In a square ABCD, A(1,3) and C(4,2). AC is a diagonal. Express the coordinates of a point on the diagonal BD using a real parameter. Hence find the coordinates of the other two vertices.

(a^2+b^2)\ab+1=4
Give a equation to solve the value of a and b.
a=? & b?

Find the equation of the plane through the line x-2÷2=y-3÷3=z-4÷5 and parallel to x-axis?

Find the equation of the plane through (2,3,-4) and (1,-1,3) and parallel to x-axis?

Find the angle between the line joining the points (3,-4,-2) and (12,2,0) and the plane 3x-y+z=1