Equation of a Circle (AQA GCSE Further Maths)

A circle, centre , touches the -axis at the point

The line  intersects the circle at the points  and 

Work out the equation of the circle.

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

The tangent at is shown.

Work out the equation of the circle.

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

The equations of the two circles shown are

and

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

......................... units²

A circle has equation   

is the point

Show that is on the circle.

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

Work out the -coordinate of .

You must show your working.

is the equation of a circle.

The point has coordinates and lies on the circle.

The point lies on the same circle such that is a diameter.

The diameter lies along a straight line, .

Find the equation of , giving your answer in the form .

 A circle has centre and equation

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 .

Show that the equation of the tangent at is

Work out the -coordinate of .

The circle with centre and radius goes through the point .

Find the two possible values of .

A tangent touches a circle at the point .

A parallel tangent touches the same circle at the point .

Find the equation of the circle.

Give your answer in the form where , and are integers.