Analytic Geometry Answers

Write the general equation of the line satisfying the given conditions:
1. passing trough (1, 0) and parallel to the line through (1/2, 3) and (0,0)
2. passing through (2, -4) and parallel to the line 3x - 7y - 11 = 0
3. passing through (-1/3, 1/2) and perpendicular to the line through (4, 1) and (-2, 7)
4. passing through (-1/2, 2) and perpendicular to the line with slope -5/2
5. passing through the point of intersection of lines 5x - 2y - 12 = 0 and x + 3y + 1 = 0 and perpendicular to the line 7x + 4y - 10 = 0.
6.The base of a triangle is the line segment from (3,0) to (2,-3). If the area of the triangle is 7, find the general equation of the locus of the third vertex. (Two solutions).

Find the distance between the given lines:
a. 3x - y = 5 and 3x - y = 25
b. 4x - 6y = 9 and 2x - 3y = 6

Find the general equation of the line passing through the given point and parallel to the indicated equation of the line:
a. (4, 1); 3X + 4Y - 10 = 0
b. (-1/2, -4); 7x - 8y - 5 = 0

Find the general equation of the line passing through the given point and perpendicular to the indicated equation of the line
a. (, 4); 4x + 4y - 11 = 0
b. (-4, -1/3); 7x - 8y -5 = 0

Find the angle of inclination of a line whose equation is
a. 6x - 5y + 30 = 0
b. 3x - 5y + 6 = 0
c. 12x - 9y = 32

Find the angle formed from line 1 to line 2:
a. line 1: 4x - 5y + = 0; line 2: 6x -4y - 12 = 0
b. line 1: 2x + 7y = 0; line 2: 3x - 5y - 15 = 0

Find the equation of the line:
1. having an x-intercept 4 and slope 5
2. through (5, -8) and with intercepts equal
3. through (-6, 3) and with intercepts numerically equal but opposite in sign
4. through (-5, 3) and with x-intercept twice the y-intercept
5. through (3, 2) and having a slope equal to two-thirds of its y-intercept
6. through (-4, -2) and with sum of intercepts 3
7. through (4, -2) and with product of intercepts -18.
8. through (4, -2) and forming with the axes a triangle of area 9 square units

Find the general equation of the line parallel to 4x - 3y = 15 and passing:
a. at a distance 2 from the origin
b. twice as far from the origin
c. 2 units far from the origin
d. at a distance 5 from the given line


Find the general equation of the line parallel to x + y = 3 and passing:
a. at a distance 2 from the origin
b. 2 square root of 2 units farther from the origin
c. 2/3 as far from the origin
d. at a distance 3 square root of 2 from the given line

Find the general equation of the line:
a. parallel to the line 2x + 3y = 6 and passing at a distance 5 square root of 13 over 13 from the point (-1, 1)
b. parallel to the line x - y + 9 = 0 and passing at a distance 5 square root of 2 from the point (1, 4)
c. perpendicular to the line 3x + 4y = 7 and passing at a distance 4 from the point (1, -2)
d. perpendicular to the line 3x - 4y = 20 and passing at a distance 2 from the point (-1, 1)

CD is trisected at points P and Q. Find the position vectors of points of trisection, if the
position vectors of C and D are c
→
and d
→
respectively

Choose the point on the terminal side of -45°.

(-3, -3)
(4, -4)
(5, 5)
(-2, 2)

: Which conic section does the equation below describe?

2x^2 + 2y^2 – 6x + 4y + 1 = 0

A: parabola
B: circle
C: ellipse
D: hyperbola

: What are the coordinates of the focus of the conic section shown below?

Write your answer without using spaces.

Y^2 + 16y – 4x + 4 = 0

Answer:_________

: Write the equation of the dircetrix of the conic section shown below. Write your answer without using spaces.

Y^2 + 16y + 4x + 4 = 0

Answer:_________

: What are the coordinates of the vertices of the conic section shown below?

(y+2)^2 (x-3)^2
---------- - ---------- = 1
16 9

A: (0, -2) and (6, - 2)
B: (-2, -1) and (-2, 7)
C: (-1, -2) and (7, - 2)
D: (3, -6) and (3, 2)


: What are the coordinates of the foci of the conic section shown below?

(y+2)^2 (x-3)^2
---------- - ----------- = 1
25 4



a: (3 ± √21, -2)

b: (3 ± √29, -2)

c: (3, -2 ± √29)

d: (3, -2 ± √21)


: Which direction does the graph of the equation shown below open?

X^2 + 6x – 4y + 5 = 0

A: up
B: down
C: right
D: left