Coordinate geometry

1. Find the gradient of the line through (-3, 7) and (5, -1).

1. -1
2. 1
3. -8
4. 8

2. Which equation is the line of gradient 3 passing through (2, -4)?

1. y = 3x + 2
2. y = 3x - 10
3. y = -3x + 2
4. y = 2x - 8

3. What is the gradient of the line 6x + 3y - 12 = 0?

1. 2
2. -1/2
3. -2
4. 6

4. Which equation represents the vertical line through (4, -7)?

1. y = 4
2. y = -7
3. x = -7
4. x = 4

5. Find p if 2x - py + 5 = 0 is parallel to y = (1/2)x - 3.

1. p = 4
2. p = -4
3. p = 1
4. p = -1

6. What is the gradient of a line perpendicular to 3x - 2y + 8 = 0?

1. 3/2
2. -2/3
3. 2/3
4. -3/2

7. Find the midpoint of the segment joining (-5, 4) and (7, -2).

1. (2, 2)
2. (1, -1)
3. (1, 1)
4. (-1, 1)

8. Find the exact distance between (1, -2) and (7, 6).

1. 8
2. sqrt(28)
3. 14
4. 10

9. Find the intersection of 2x + y = 11 and x - y = 1.

1. (4, 3)
2. (3, 4)
3. (5, 1)
4. (2, 7)

10. State the centre and radius of (x + 2)^2 + (y - 5)^2 = 49.

1. Centre (2, -5), radius 7
2. Centre (-2, 5), radius 7
3. Centre (-2, 5), radius 49
4. Centre (2, 5), radius 7

11. Which standard form is equivalent to x^2 + y^2 - 8x + 6y = 0?

1. (x - 4)^2 + (y + 3)^2 = 7
2. (x + 4)^2 + (y - 3)^2 = 25
3. (x - 4)^2 + (y + 3)^2 = 25
4. (x - 8)^2 + (y + 6)^2 = 100

12. Relative to x^2 + y^2 = 20, where is the point (2, 3)?

1. On the circle
2. Outside the circle
3. At the centre
4. Inside the circle

13. A circle has diameter endpoints (-2, 1) and (4, 5). What is its equation?

1. (x - 1)^2 + (y - 3)^2 = 13
2. (x - 1)^2 + (y - 3)^2 = 52
3. (x + 1)^2 + (y + 3)^2 = 13
4. (x - 2)^2 + (y - 4)^2 = 13

14. Find the tangent to x^2 + y^2 = 25 at the point (3, 4).

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

15. How many points of intersection do y = 6 and x^2 + y^2 = 25 have?

1. Two
2. One
3. None
4. Infinitely many

16. Find the intersections of y = x - 1 with x^2 + y^2 = 5.

1. (1, 0) and (2, 1)
2. (0, -1) and (1, 0)
3. (-2, -3) and (1, 0)
4. (-1, -2) and (2, 1)

17. For which values of k is y = x + k tangent to x^2 + y^2 = 10?

1. k = 2sqrt(5) or k = -2sqrt(5)
2. k = sqrt(5) only
3. k = 5 or k = -5
4. k = 10 or k = -10

18. For which values of k does y = k not meet (x - 2)^2 + (y + 1)^2 = 16?

1. -5 < k < 3
2. k < -5 or k > 3
3. k <= -5 or k >= 3
4. k = -5 or k = 3

19. The chord x = 3 cuts x^2 + y^2 = 25 at two points. What is the chord's midpoint?

1. (0, 3)
2. (3, 4)
3. (3, 0)
4. (4, 0)

20. A(0, 0) and B(6, 0) are endpoints of a diameter, and P is any other point on the circle. What is angle APB?

1. 30 degrees
2. 45 degrees
3. 60 degrees
4. 90 degrees

21. What line contains the common points of x^2 + y^2 = 25 and (x - 4)^2 + y^2 = 9?

1. x = 4
2. y = 4
3. x = 2
4. y = 2

22. A circle's centre lies on x + y = 4 and x - y = 2, and the circle passes through (6, 5). What is its equation?

1. (x - 3)^2 + (y - 1)^2 = 5
2. (x - 3)^2 + (y - 1)^2 = 25
3. (x + 3)^2 + (y + 1)^2 = 25
4. (x - 6)^2 + (y - 5)^2 = 25

23. How many intersections are there between y = 2x + 1 and y = x^2 - 2?

1. None
2. One
3. Two
4. Infinitely many

24. Find k if the line y = kx is tangent at the origin to (x - 3)^2 + (y - 4)^2 = 25.

1. k = 3/4
2. k = 4/3
3. k = -4/3
4. k = -3/4