Analytic Geometry Answers

5) If A= (51 i – 14 j + 43k ) cm and B = ( -31i -21j-11k) mm ;
a) Find D= -A+3B.
b) Find the magnitude D.

Find the equation of the line which is twice as far from the line 3x+4y-6=0 as from 4x+3y-5=0

The sides of a triangle lie on the lines 3x+4y+8=0 , 3x-4y-32=0 & x=8.
Find the equation of the circle inscribe in the triangle.

Triangle ABC is rotated to create the image A'B'C'.


Which rule describes the transformation?

Find the image of triangle ABC, for A(3, 3), B(9, 3) and C(6, 7), after a glide reflection described. Translation (x, y) maps to (x, y + 1) ; Reflection in y = 1

Find the equation of the circle determined by the given conditions:
10. tangent to the x-axis and passing through (5, 1) and (12, 8)
11. tangent to the line y= -1 and containing the points (1, 1) and (3, 3)
12. tangent to the lines 2x + y = 4, 2x + y =2 and x - 2y + 5 = 0
13. passing through the origin and tangent to the lines 3x + 4y - 10 = 0 and 4x + 3y - 5 = 0
14. inscribed in a triangle with sides on the lines x - 3y = -5, 3x + y = 1 and 3x - y = -11
15. inscribed in a triangle whose vertices are (0, 6), (8, 6), and (0, 0)
16. having radius of square root of 5, through (0, 4) and (3, 7).
17. radius and tangent to the line 2x + y -1 = 0 at (1, -1)
18. tangent to 3x - 2y - 9 = 0 and 2x - 3y - 1 = 0 and center on 2x + y - 10 = 0

Find the equation of the circle determined by the given conditions:
1. passing through (1, 2), (2, 3) and (-2, 1)
2. passing through (4, 6), (-2, -2) and (-4, 2)
3. circumscribing a triangle formed by the lines x - y + 2 = 0, 2x + 3y - 1 = 0 and 4x + y + 17 = 0
4. center of the x-axis and passing through (0, 0) and (2, 4)
5. containing the point (2, 2) and tangent to the lines y = 1 and y = 6.
6. tangent to the x-axis and passing through (5, 1) and (-2, 8)
7. passing through (-3, -1), (3, -5) and having its center on the line 2x - y - 2 = 0
8. tangent to the line 4x - 3y = 6 at (3, 2) and passing through (2, -1)
9. tangent to the line 3x - 4y - 5 = 0 at (3, 1) and passing through (-3, -1)

Write the equation of the circle satisfying the given equations:
1. with center (2, -1) and radius 3.
2. with center (1, 0) and radius square root of 5 over 3
3. with center (0, 0) and diameter 8.
4 with center (3, 4) and passing through (-1, 1).
5. center at (-3, 2) and touching the x-axis
6. center at (4, 1) touching the y-axis.
7. with radius 3, touching both axes and center in 3rd quadrant.
8. with radius 2, tangent to both axes and center in 4th quadrant.
9. with center at (0, 3) and touching the line x - y = 0
10. with center at (-2, -1) and tangent to the line 4x - 3y = 12.
11. with center at (3,2) and tangent to the line passing through (-1, 3) and (-4,0)

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.

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)