# AS Maths - Core 1 - Solomon Worksheets - Circles - Worksheet C - Mixed 'Exam-style' Questions

Practice worksheets for Core 1 topic cirles

Teacher recommended

- Created by: Charlotte Wilding
- Created on: 17-05-12 11:47

First 338 words of the document:

C1 CIRCLES Worksheet C

1 A circle has the equation x2 + y2 - 8x + 7 = 0.

a Find the coordinates of the centre of the circle. (2)

b Find the radius of the circle. (2)

2 A circle has the equation x2 + y2 - 6x + 2y - 15 = 0.

a Find the coordinates of the centre of the circle. (2)

b Find the radius of the circle. (1)

c Show that the tangent to the circle at the point (7, 2) has equation

4x + 3y - 34 = 0. (4)

3 A circle has the equation x2 + y2 + 6x - 8y + 21 = 0.

a Find the coordinates of the centre and the radius of the circle. (3)

The point P lies on the circle.

b Find the greatest distance of P from the origin. (2)

4 y

x2 + y2 = 50 A

O x

C

B

The diagram shows the circle with equation x2 + y2 = 50 and the tangents to the circle

at the points A (5, 5) and B (1, -7).

a Find an equation of the tangent to the circle at A. (3)

b Show that the tangent to the circle at B has the equation

x - 7y - 50 = 0. (3)

c Find the coordinates of the point C where the tangents to the circle at A and B intersect. (2)

5 Circle C1 has the equation x2 + y2 - 2ay = 0, where a is a positive constant.

a Find the coordinates of the centre and the radius of C1. (4)

Circle C2 has the equation x2 + y2 - 2bx = 0, where b is a constant and b > a.

b Sketch C1 and C2 on the same diagram. (4)

6 The circle C has the equation x2 + y2 + 2x - 14y + 30 = 0.

a Find the coordinates of the centre of C. (2)

b Find the radius of C, giving your answer in the form k 5 . (2)

c Show that the line y = 2x - 1 is a tangent to C and find the coordinates of the point

of contact. (4)

Solomon Press

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