Equation of a Circle (AQA GCSE Further Maths)

A circle, centre (0, 0) has circumference 20

Work out the equation of the circle.

[2]

A circle, centre (4, –2), passes through the origin and point A (8, 0) on the -axis.

The tangent at is shown.

Work out the equation of the circle.

[2]

Work out the equation of the tangent to the circle at .

[3]

The equations of the two circles shown are

and

Work out the shaded area.
Give your answer as an integer multiple of .

.........................units² [3]

 A circle has centre C and equation

(4, –7) and are points on the circle.

The tangent at is parallel to the -axis.

The tangents at and intersect at point .

Write down the coordinates of .

[1]

Show that the equation of the tangent at is

[1]

Work out the -coordinate of .

[4]

A circle has centre (−1, 2) and radius 5

Which of these is the equation of the circle?
Tick one box.

[1]

A circle has equation       

P is the point (–5, 2)

Show that P is on the circle.

[1]

The tangent to the circle at P intersects the -axis at point Q.

Work out the -coordinate of Q.
You must show your working.

[4]

The equation of a circle is  

What are the coordinates of the centre of the circle?

Circle your answer.

(-5 , -8)      (-5 , 8)      (5 , 8)      (5 , -8)

[1]

Write down the radius of the circle.   

[1]