Coordinate geometry

Practice sheet

Fresh questions from the whole chapter, to do on paper.

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  1. Find the distance between (−1,−3)(-1, -3) and (2,1)(2, 1).
  2. Tap the midpoint of the segment from (−6,−5)(-6, -5) to (−4,−1)(-4, -1).
  3. Find the exact distance between (0,−2)(0, -2) and (1,−4)(1, -4).
  4. What is the radius of the circle (x−9)2+(y+1)2=16(x - 9)^2 + (y + 1)^2 = 16?
  5. Which is the equation of the circle with center (2,−8)(2, -8) and radius 7?
    1. (x−2)2+(y+8)2=49(x - 2)^2 + (y + 8)^2 = 49
    2. (x+2)2+(y−8)2=49(x + 2)^2 + (y - 8)^2 = 49
    3. (x−2)2+(y+8)2=7(x - 2)^2 + (y + 8)^2 = 7
  6. The parabola x2=8yx^2 = 8y has its focus at (0,c)(0, c). What is cc?
  7. The parabola y2=8xy^2 = 8x has the directrix x=dx = d. What is dd?
  8. A parabola has focus (0,3)(0, 3) and directrix y=−3y = -3. Its equation is x2=kyx^2 = ky. What is kk?
  9. A line has slope 1/81/8. Find the slope of a line perpendicular to it.
  10. Are the lines y=6x+1y = 6x + 1 and y=−16x+5y = -\tfrac{1}{ 6 }x + 5 parallel, perpendicular or neither?
    1. Perpendicular: the product of the slopes is −1
    2. Parallel
    3. Neither
  11. Find the slope of the line through (0,5)(0, 5) and (−5,−3)(-5, -3).
  12. Find the yy-intercept of the line parallel to y=−3x+−1y = -3x + -1 through (−3,−5)(-3, -5).