The Circle & Its Tangent (Grade 12) — Worksheet & Memo

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Grade 12 · Analytical Geometry

The Circle & Its Tangent (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 18

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the centre and radius of (x − 2)² + (y + 3)² = 25.
(2)
Centre (2 ; −3), radius 5✓✓ (2)
2
Determine the centre and radius of x² + y² − 4x + 6y − 12 = 0.
(4)
Completing the square: (x − 2)² + (y + 3)² = 25 → centre (2 ; −3), r = 5✓✓✓✓ (4)
3
Show that P(6 ; 0) lies on the circle x² + y² − 4x + 6y − 12 = 0.
(2)
(6 − 2)² + (0 + 3)² = 16 + 9 = 25 = r², so P lies on the circle.✓✓ (2)
4
Determine the gradient of the radius MP where M(2 ; −3) and P(6 ; 0).
(2)
3/4✓✓ (2)
5
Determine the equation of the tangent to the circle at P(6 ; 0).
(3)
m = −4/3 → y = −4/3x + 8✓✓✓ (3)
6
Write down the equation of a circle with centre (0 ; 0) and radius 7.
(1)
x² + y² = 49✓ (1)
7
Determine the radius of x² + y² + 2x − 8y + 8 = 0.
(3)
(x + 1)² + (y − 4)² = −8 + 1 + 16 = 9 → r = 3✓✓✓ (3)
8
What is the relationship between a tangent and the radius at the point of contact?
(1)
They are perpendicular.✓ (1)

TOTAL: 18 marks