Question The straight line L has equation and the curve C has equation a. Sketch on the same axes the line L and the curve C, showing the values of the intercepts on the x-axis and the y-axis. b. Show that the x-coordinates of the points of intersection of L and C satisfy the equation . c. Hence find the coordinates […]
Question The circle S has centre C(8,13) and touches the x-axis, as shown in the diagram. a. Write down an equation for S, giving your answer in the form b. The point P with coordinates (3,1) lies on the circle. i. Find the gradient of the straight line passing through P and C. ii. Hence […]
Question The curve with equation is sketched below. The points A(-2,0) , B(2,0) and C(1,15) lie on the curve. a. Find an equation of the straight line AC . b. i. Find . ii. Hence calculate the area of the shaded region bounded by the curve and the line AC . Solution a. We are required to […]
Question The curve C has equation . The line L has equation , where k is a constant. a. Show that the x-coordinates of any points of intersection of the line L with the curve C satisfy the equation b. The curve C and the line L intersect in two distinct points. Show that c. Solve the inequality […]
Question A circle with centre C has equation . a. By completing the square, express this equation in the form b. Write down: i. the coordinates of C; ii. the radius of the circle, leaving your answer in surd form. c. A line has equation . i. Show that the x-coordinate of any point of intersection of […]
Question The triangle ABC has vertices A(-2,3), B(4,1) and C(2,-5). a. Find the coordinates of the mid-point of BC . b. i. F ind the gradient of AB, in its simplest form. ii. Hence find an equation of the line AB , giving your answer in the form , where q and r are […]