Analytic Geometry Answers

If the position vector of one end of a chord through the focus of the parabola y^2 = 8x is 1/2i + 2j, find the position vector of the other end.

Express the following equations of a parabola in standard form and in each case state the coordinates of its vertex,focus and the ends of the latus rectum.

(a) x^2− 2x − 4y = 0,

(b) y^2 + 12x − 48 = 0,

(c) x^2 − 6x − 2y + 7 = 0.

Write down the Cartesian equation of a parabola with vertex at the origin and the

focus at the point (0, −2).

Write the equation of the ellipse which satisfies the given conditions.

1a. Center (2, 3), horizontal axis 8, vertical axis 4

b. Center (1, -2), horizontal major axis 8, eccentricity

2a. Foci (-2,1) and (4, 1), major axis 10

b. Foci (-3,0) and (-3, 4), minor axis 6

3a. Foci (-2,2) and (4,2), eccentricity

b. Foci (+2, 0), directrices x = +8

4a. Focus (0,0), vertex (5,0), eccentricity 0.5

b. Focus (0,0), vertex (0, 2), eccentricity 0.6

5a. Center (1,3), V(1,-1), and passing through the origin

b. Center (1, 1), V(3, 1), and passing through the origin

Find the equation of the right circular cone whose vertex is (2, 1, 0), semivertical angle is 30° and the axis is the line x-2/3=y-1/1=z/2

(3.1) Find an expression for 12 || ~ u + ~ v || 2 + 12 || ~ u − ~ v || 2 in terms of || ~ u || 2 + || ~ v || 2

(3.2) Find an expression for || ~ u + ~ v || 2 − || ~ u − ~ v || 2 in terms of ~ u · ~ v

3.3) Use the result of (3.2) to deduce an expression for || ~ u + ~ v || 2 whenever ~ u and ~ v are orthogonal

to each other.

In a cartesian plane xy.The line which passes through the origin and is perpendicular to the line of equation 5x-3y-1=0 has for equation?

A. 3x-5x=0

B. 3x+5y=0

C. 5x-3y=0