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Analytic Geometry
A circle of radius square root of 10 touches the line x - 3y = 2. Find the general equation of the locus of its center. (Two solutions)
Find the general equations of the bisectors of the angles between the lines:
a. 3x + y = 6 and x + 3y = -2
b. 4x - 5y = 26 and 5x + 4y = 20
Find the general equation of the line through the point A(-1, 2) and passing at a distance 3 from the point Q(-10, -5).
A circle of radius 6 touches both the coordinate axes. A line with slope -3/4 passes over and just touches the circle. If the circle is in the first quadrant, find the general equation of the line.
Find the general equations of the bisectors of the angles between the lines:
a. 3x + y = 6 and x + 3y = -2
b. 4x - 5y = 26 and 5x + 4y = 20
Find the general equation of the line through the point A(-1, 2) and passing at a distance 3 from the point Q(-10, -5).
A circle of radius 6 touches both the coordinate axes. A line with slope -3/4 passes over and just touches the circle. If the circle is in the first quadrant, find the general equation of the line.
Analytic Geometry
Two sides of a square lie along the lines 4x + 3y = 15 and 4x + 3y = 5. Find the area of the square.
Two sides of a square lie along the lines 8x - 6y = 48 and 4x - 3y = 12. Find the perimeter of the line square.
Find the directed distance from the line to the point:
a. x = y = 5; (-2, -1)
b. x = 4y x = 4y; (3, 1)
c. 12x + 5y + 56 = 0; (-2, 4)
How far is the line from the indicated point:
a. 2x - 3y - 12 = 0; (-1, 2)
b. 5x + 12y + 56 = 0; (-2, 4)
Two sides of a square lie along the lines 8x - 6y = 48 and 4x - 3y = 12. Find the perimeter of the line square.
Find the directed distance from the line to the point:
a. x = y = 5; (-2, -1)
b. x = 4y x = 4y; (3, 1)
c. 12x + 5y + 56 = 0; (-2, 4)
How far is the line from the indicated point:
a. 2x - 3y - 12 = 0; (-1, 2)
b. 5x + 12y + 56 = 0; (-2, 4)
Analytic Geometry
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
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
Analytic Geometry
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
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
Analytic Geometry
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
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
Analytic Geometry
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)
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)
Analytic Geometry
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
position vectors of C and D are c
→
and d
→
respectively
Analytic Geometry
Choose the point on the terminal side of -45°.
(-3, -3)
(4, -4)
(5, 5)
(-2, 2)
(-3, -3)
(4, -4)
(5, 5)
(-2, 2)
Analytic Geometry
: Which conic section does the equation below describe?
2x^2 + 2y^2 – 6x + 4y + 1 = 0
A: parabola
B: circle
C: ellipse
D: hyperbola
2x^2 + 2y^2 – 6x + 4y + 1 = 0
A: parabola
B: circle
C: ellipse
D: hyperbola
Analytic Geometry
: 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 your answer without using spaces.
Y^2 + 16y – 4x + 4 = 0
Answer:_________
