O is the centre of the circle A is the point (5, 12) a) What is the equation of the circle? (2) b) Find the gradient of the radius OA. (1) b) Find the gradient of the tangent at A. (2) c) Find the equation of the tangent which passes through A. (2) 2. The diagram shows the circle + = 10 x² y² F P lies on the circle and has co-ordinate 3 x The tangent at P intersects the at Q. y-axis a) Find the gradient of the radius OP. (2) b) Find the equation of the tangent to the circle passing through P. (3) c) Work out the co-ordinates of Q. (2) 3. P (-1, 4) is a point on a circle, centre (0, 0). M a) Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c. (4) b) The tangent cuts the axis at the point Q. x Find the area of triangle OQP. (3) 4. L is the circle with equation M P = is a point on the circle L. Find the equation of the tangent to L at the point P. (4)
O is the centre of the circle A is the point (5, 12) a) What is the equation of the circle? b) Find the gradient of the radius OA. b) Find the gradient of the tangent at A. c) Find the equation of the tangent which passes through A. (2) (1) (2) (2) 2. F The diagram shows the circle x² + y² = 10 P lies on the circle and has x co-ordinate 3 The tangent at P intersects the y-axis at Q. a) Find the gradient of the radius OP. b) Find the equation of the tangent to the circle passing through P. c) Work out the co-ordinates of Q. (2) (3) (2) 3. M P (-1, 4) is a point on a circle, centre (0, 0). a) Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c. b) The tangent cuts the x axis at the point Q. Find the area of triangle OQP. (4) (3) 4. M L is the circle with equation P = is a point on the circle L. Find the equation of the tangent to L at the point P. (4)