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.

Find the midpoint and distance of the line segment that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) c) (-4.5, -12.5) and (4.5, 13)

1.) Find an equation for the plane that passes through the origin (0, 0, 0) and is parallel to the plane - x + 3y - 2z = 6

2.) Find the distance between the point (-1, - 2, 0) and the plane 3x - y + 4z =-2

1. Find the distance between the point and given plane.

P (1, 2, 3)

𝝅: 2x + y – 2z – 4 = 0

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.

A slender rod 40 in long is bent so as to form a right triangle. If the segments are 8 in and 32 in long, find the centroid.

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