Analytic Geometry Answers

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.

Which of the following statements is/are true? Explain why the false one is false. A. If u = (u1; u2) with ui not eqaual to 0 for some 1 <= i <= 2; then the unit vector in the direction of u is 1/sqrt( u1^2 +u2^2 )(u1; u2) : (2) B. u = (1; 2; 3) is the unit vector in the direction of u: (

Find the plane that passes through the point (2,5,3) and is perpendicular to the plane 2x-3y+4z+7=0