Equation of a circle

22The equation of circle A is x² + y² = 25 Circle A is translated by the vector 02 to give circle B. Sketch circle B. Show the coordinates of the centre of circle B and the points where circle B meets the y-axis.

C is a circle with centre (0, 0) The straight line with equation 3 x – 2 y = 52 is the tangent to C at the point P. Find the coordinates of P.

C is the circle with equation x² + y² = 4 Find an equation of the tangent to C at the point (p, 1) where p 0

C is a circle with centre (0, 0) L is a straight line. The circle C and the line L intersect at the points P and Q. The coordinates of P are (5, 10) The x coordinate of Q is –2 L has a positive gradient and crosses the y-axis at the point (0, k) Find the value of k.

On the grid, draw the graph of x² + y² = 169

Use your graph to find estimates for the solutions of the simultaneous equations

2 y = 3 x

23A circle has equation x² + y² = 25 The point P with coordinates (–3, 4) lies on the circle. Alex says that the tangent to the circle at P crosses the x-axis at the point (–8, 0) Is Alex correct? You must show how you get your answer.

24A circle has equation x² + y² = 12.25 The point P lies on the circle. The coordinates of P are (2.1, 2.8) The line L is the tangent to the circle at point P. Find an equation of L. Give your answer in the form ax + by = c, where a, b and c are integers.

The centre of a circle is the point with coordinates (−1, 3) The point A with coordinates (6, 8) lies on the circle. Find an equation of the tangent to the circle at A. Give your answer in the form ax + by + c = 0 where a, b and c are integers.

C is a circle with centre the origin. A tangent to C passes through the points (–20, 0) and (0, 10) Work out an equation of C. You must show all your working.

The diagram shows a circle, centre O.

AB is the tangent to the circle at the point A. Angle OBA 30° Point B has coordinates (16, 0) Point P has coordinates (3 p, p) Find the value of p. Give your answer correct to 1 decimal place. You must show all your working.

The equation of a circle is x² + y² = 42.25

Find the radius of the circle.

On the grid, draw the graph of x² + y² = 12.25

Hence find estimates for the solutions of the simultaneous equations

2 x + y = 1

L is the circle with equation x² + y² = 4

Find an equation of the tangent to L at the point P.

The equation of a curve is y = a^x A is the point where the curve intersects the y-axis.

State the coordinates of A.

The equation of circle C is x² + y² = 16

Draw a sketch of circle B.

Label with coordinates the centre of circle B and any points of intersection with the x-axis.