Equation of a circle

The diagram shows a circle, centre (0, 0).

Write down the equation of the circle.

Point A has coordinates (2.3, 3.3).

Show that point A does not lie on the circle and state, with a reason, whether it lies inside the circle or outside the circle.

Point A lies........ the circle because........

The graph of y =-3x intersects the graph of x² + y² = 70 at two points.

Work out the exact coordinates of the two points. You must show your working.

(........,........) and (........,........)

The diagram shows a circle, centre the origin, with the tangent to the circle at the point (4, 2).

Write down the equation of the circle.

Show that the tangent to the circle at the point (4, 2) has gradient - 2.

Find the equation of the tangent to the circle at the point (4, 2).

Describe fully the graph of x² + y² = 20.

The graph of y = 3x + 10 intersects the graph of x² + y² = 20 at two points.

Use an algebraic method to work out the coordinates of the two points. You must show your working.

(b) (........,........) and (........,........)

A circle has equation x² + y² = 100. The sketch shows the circle and two points, A and B, which lie on the circumference of the circle.

Write down the coordinates of point A.

Point B has x-coordinate 3.

Find the exact value of the y-coordinate of point B.

Another point, C, lies on the circle and has a y-coordinate that is seven times its x-coordinate.

Find the two possible pairs of coordinates for point C. Give your answers in exact form. You must show your working.

(c) (…….……., …….…….) and (…….……., ……….….)

The diagram shows a circle, centre the origin.

Write down the equation of the circle.

The graph below shows a circle with centre (0, 0) and equation x² + y² = 169.

Show that the point (- 12, 5) lies on the circumference of the circle.

Find the equation of the tangent to the circle at the point (- 12, 5), giving your answer in the form y = mx + c.

Find the equation of the circle.

Here is a sketch of the circle x² + y² = 45.

Find the equation of the tangent at the point (-3, 6).

In this question all units are in cm.

A circle has equation x² + y² = 36.

Write down the radius and centre of the circle.

(a) radius:........ cm

Work out the length AB.

The point (- 5, 2) lies on the circumference of a circle, centre (0, 0).

Find the equation of the circle.

Work out the gradient of the tangent to the circle at (- 5, 2).

Find the exact coordinates of the two intersections of the line y = 2x and the circle x² + y² = 30

(........,........) and (........,........)

The diagram shows a circle, centre the origin.

Write down the equation of the circle.

Point P has coordinates (8, –6).

Show that point P lies on the circle.

Find the equation of the tangent to the circle at point P.

Describe fully the graph which has the equation x² + y² = 9.