Analytic Geometry Answers

2 Given that A1=3i−2j+k,A2=2i−4j−3k,A3=−i+2j+2k, find the magnitudes of 2A1−3A2−5A3
3 Given that A1=2i−j+k,A2=i+3j−2k,A3=3i+2j+5kand A4=3i+2j+5k,Find scalars a, b, c suchthat A4=aA1+bA2+cA3
5 A car travels 3km due north, then 5km northeast. Determine the resultant displacement
6 If A1=3i−j−4k, A2=−2i+4j−3k,A3=i+2j−k, find |3A1−2A3+4A3|

Find the standard equation of the circle touching the line x + 2y = 8 at (0, 4) and passing through (3, 7).

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)