Analytic Geometry Answers

3x + 8y = 4
(8, -9)
a. Find the equation of a line passing through the point given perpendicular to the line given.
b. Find the distance between the point and the line.
c. Find the equation of a line passing through the point (4, 3) parallel to the line given and its distance.

3x - 4y + 3 = 0
6x - 8y +7 = 0
a. Find the distance between the two lines.
b. Find the equation of the perpendicular line passing through. (-6,4)
c. Determine the distance of 2 given equations to point (-6.4)

Find the area of the circle whose equation is x2
+ y2
= 6x – 8y.

Given the equation of a circle x
2
+ y2
– 14x – 16y + 88 = 0. Determine the following
a. Center of the circle
b. Radius
c. Area
d. Perimeter

Given the vertex and focus of a parabola, (4,2) and (4,5). Determine the following
a. General equation
b. Standard equation
c. Location of the opening
d. Location of the directrix (coordinate)

QUESTION 8 8.1 Let L1 and L2 be lines defined by x = w0 + su, s ∈ R and y = w1 + tv, t ∈ R, respectively. Show that L1and L2 are parallel if and only if u = kv for some k ∈ R. (8) 8.2 Find the plane that passes through the point (2, 4, −3) and is parallel to the plane −2x + 4y − 5z + 6 = 0. (4) 8.3 Find the line that passes through the point (2, 5, 3) and is perpendicular to the plane 2x − 3y + 4z + 7 = 0. (4) 8.4 Find an equation of the plane passing through the point(−2, 3, 4) and is perpendicular to the line passing through the points (4, −2, 5) and (0, 2, 4). (4)

determine whether the line through the pair of points A, B is
parallel or perpendicular to the line through the pair C, D.
3.) A(1,5), B(-7,1) and C(8,-2), D(4,6)
4.) A(6,2), B(8,6) and C(4,8), D(2,4)

Find the equation of the circle whose center is at (3, -5) and whose radius is 4

3x - 4y + 3 = 0
6x - 8y +7 = 0
a. Find the distance between the two lines.
b. Find the equation of the perpendicular line passing through. (-6,4)
c. Determine the distance of 2 given equations to point (-6.4)

3x + 8y = 4
(8, -9)
a. Find the equation of a line passing through the point given perpendicular to the line given.
b. Find the distance between the point and the line.
c. Find the equation of a line passing through the point (4, 3) parallel to the line given and its distance.