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Grade 12 · Analytical Geometry
The Circle & Its Tangent (Grade 12)
EXAM-STYLE CLASS TEST
Marks
32
Duration
50 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 32
Instructions and Information
- Answer ALL the questions in this question paper.
- Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
- Show ALL calculations clearly.
- Show all units where applicable.
- Number the answers correctly according to the numbering system used in this question paper.
- A non-programmable calculator may be used, unless stated otherwise.
- Write neatly and legibly.
Question 1
[10 MARKS]Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.
- 1.1A circle with centre (a ; b) and radius r has equation …(1)A)(x − a)² + (y − b)² = r²B)(x + a)² + (y + b)² = r²C)(x − a)² + (y − b)² = rD)(x − a)² − (y − b)² = r²
- 1.2The centre of (x − 3)² + (y + 2)² = 25 is …(1)A)(3 ; −2)B)(−3 ; 2)C)(3 ; 2)D)(−3 ; −2)
- 1.3The RADIUS of (x − 3)² + (y + 2)² = 25 is …(1)A)5B)25C)12,5D)√5
- 1.4x² + y² − 6x + 4y − 12 = 0 has centre …(1)A)(3 ; −2)B)(−6 ; 4)C)(−3 ; 2)D)(6 ; −4)
- 1.5The radius of x² + y² − 6x + 4y − 12 = 0 is …(1)A)5B)12C)25D)√12
- 1.6A tangent to a circle at a point P is PERPENDICULAR to …(1)A)the radius drawn to PB)any chord through PC)every diameter of the circleD)the x-axis
- 1.7A circle has centre C(2 ; 1) and P(5 ; 5) lies on it. Its radius is …(1)A)5B)7C)25D)√7
- 1.8The gradient of the radius from C(2 ; 1) to P(5 ; 5) is …(1)A)43B)34C)−34D)−43
- 1.9So the gradient of the TANGENT at P(5 ; 5) is …(1)A)−34B)43C)34D)−43
- 1.10The equation of that tangent at P(5 ; 5) is …(1)A)4y = −3x + 35B)4y = 3x + 5C)3y = −4x + 35D)y = −3x + 5
Answer grid — circle your answers for Question 1
| 1.1 | A | B | C | D |
| 1.2 | A | B | C | D |
| 1.3 | A | B | C | D |
| 1.4 | A | B | C | D |
| 1.5 | A | B | C | D |
| 1.6 | A | B | C | D |
| 1.7 | A | B | C | D |
| 1.8 | A | B | C | D |
| 1.9 | A | B | C | D |
| 1.10 | A | B | C | D |
Question 2
[12 MARKS]A circle has the equation x2 + y2 − 4x + 6y − 12 = 0.
- 2.1Determine the coordinates of the centre and the length of the radius by completing the square.(5)
- 2.2Show that the point (5 ; 1) lies on the circle.(2)
- 2.3Determine the equation of the tangent to the circle at (5 ; 1).(5)
Question 3
[10 MARKS]Answer the questions below about the same circle.
- 3.1Determine the coordinates of the point on the circle DIAMETRICALLY opposite (5 ; 1).(3)
- 3.2Determine whether the point (6 ; 1) lies inside, on, or outside the circle. Justify with a calculation.(4)
- 3.3Write down the equation of the circle with the same centre but twice the radius.(3)
TOTAL: 32 marks
This question paper consists of 3 questions.