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Grade 12 · Analytical Geometry
The Circle & Its Tangent (Grade 12)
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  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Write down the centre and radius of (x − 2)² + (y + 3)² = 25.
    (2)
    −4−22468−8−6−4−22Mxy
  2. 2
    Determine the centre and radius of x² + y² − 4x + 6y − 12 = 0.
    (2)
    M(2 ; -3)P(6 ; 0)xy
  3. 3
    Show that P(6 ; 0) lies on the circle x² + y² − 4x + 6y − 12 = 0.
    (2)
    M(2 ; -3)P(6 ; 0)xy
  4. 4
    Determine the gradient of the radius MP where M(2 ; −3) and P(6 ; 0).
    (2)
    −4−22468−8−6−4−22M(2 ; −3)P(6 ; 0)xy
  5. 5
    Determine the equation of the tangent to the circle at P(6 ; 0).
    (2)
    M(2 ; -3)P(6 ; 0)xy
  6. 6
    Write down the equation of a circle with centre (0 ; 0) and radius 7.
    (2)
    −8−6−4−22468−8−6−4−22468M(0 ; 0)xy
  7. 7
    Determine the radius of x² + y² + 2x − 8y + 8 = 0.
    (2)
    −5−4−3−2−1123−112345678Mxy
  8. 8
    What is the relationship between a tangent and the radius at the point of contact?
    (2)
    M(2 ; -3)P(6 ; 0)xy
TOTAL: 16 marks
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