Elective Mathematics

Question 1

1Find the gradient of the tangent to x² + y² = 61 at the point (5, 6).

Hard

A. −5/6 B. 5/6 C. −6/5 D. 6/5

Question 2

2The radius of the circle x² + y² = 36 is ___

Easy

Your answer (fill in the blank)

Question 3

3Find the radius of the circle x² + y² − 8x − 10y + 25 = 0.

Medium

A. 5 B. 16 C. 25 D. 4

Question 4

4The tangent is perpendicular to the radius at the point of contact.

Easy

A. True B. False

Question 5

5The centre of x² + y² + 2gx + 2fy + c = 0 is

Easy

A. (g, f) B. (−f, −g) C. (−g, −f) D. (g, −f)

Question 6

6Write down the equation of the circle with centre (5, 3) and radius 7.

Easy

A. (x − 5)² + (y − 3)² = 49 B. x² + y² = 49 C. (x − 5)² + (y − 3)² = 7 D. (x + 5)² + (y + 3)² = 49

Question 7

7A circle has exactly one centre.

Easy

A. True B. False

Question 8

8The general equation of a circle is

Easy

A. x² + y² + 2gx + 2fy + c = 0 B. ax + by + c = 0 C. x² + y² = 2r D. y = mx + c

Question 9

9Find the centre of the circle x² + y² + 8x − 6y − 11 = 0.

Medium

A. (8, −6) B. (3, −4) C. (4, −3) D. (−4, 3)

Question 10

10The radius of the circle x² + y² = 49 is ___

Easy

Your answer (fill in the blank)