# AS Maths - Core 1 - Solomon Worksheets - Circles - Worksheet B - Further Questions

Practice worksheets for Core 1 topic cirles

Teacher recommended

- Created by: Charlotte Wilding
- Created on: 17-05-12 09:00

First 335 words of the document:

C1 CIRCLES Worksheet B

1 The circle C has centre (3, -2) and radius 5.

a Write down an equation of C in cartesian form.

The line y = 2x - 3 intersects C at the points A and B.

b Show that AB = 4 5 .

2 The line AB is a diameter of circle C.

Given that A has coordinates (-5, 6) and B has coordinates (3, 8), find

a the coordinates of the centre of C,

b a cartesian equation for C,

c an equation of the tangent to C at A.

3 The circle C has equation x2 + y2 + 8x - 16y + 62 = 0.

a Find the coordinates of the centre of C and the exact radius of C.

The line l has equation y = 2x + 1.

b Show that the minimum distance between l and C is 3( 5 - 2) .

4 y

S

C2

P C1

R

Q

O x

The diagram shows rectangle PQRS and circles C1 and C2.

Each circle touches the other circle and three sides of the rectangle. The coordinates of the

corners of the rectangle are P (0, 4), Q (1, 1), R (7, 3) and S (6, 6).

a Find the radius of C1.

b Find the coordinates of the point where the two circles touch.

c Show that C1 has equation 2x2 + 2y2 - 8x - 12y + 21 = 0.

5 The circle C touches the y-axis at the point A (0, 3) and passes through the point B (2, 7).

a Find an equation of the perpendicular bisector of AB.

b Find an equation for C.

c Show that the tangent to C at B has equation

3x - 4y + 22 = 0.

6 The point P (x, y) moves such that its distance from the point A (-3, 4) is twice its distance from

the point B (0, -2).

Show that the locus of P is a circle and find the coordinates of the centre and the exact radius of

this circle.

Solomon Press

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