Question The points Q (1, 3) and R (7, 0) lie on the line , as shown in Figure. The length of QR is . a. Find the value of a. The line l2 is perpendicular to , passes through Q and crosses the y-axis at the point P, as shown in Figure. Find b. an […]
Question The curve C has equation , where k is a constant. a. Find . Point A with x-coordinate lies on C. The tangent to C at A is parallel to the line with equation . Find b. The value of k. c. The value of y-coordinate of A. Solution a. Gradient (slope) of the curve […]
Question The curve C has equation y=(x + 3)(x −1)2 . a. Sketch C showing clearly the coordinates of the points where the curve meets the coordinate axes. b. Show that the equation of C can be written in the form y = x3 + x2 − 5x + k, where k is a positive integer, and […]
Question The curve C has equation y = f(x), x > 0, and . Given that the point P(4,1) lies on C, a. find f(x) and simplify your answer. b. Find an equation of the normal to C at the point P(4, 1). Solution a. We are required to find f(x), when; We are also given that […]
Question The point A(–6, 4) and the point B (8, –3) lie on the line L. a. Find an equation for L in the form ax + by + c = 0, where a, b and c are integers. b. Find the distance AB, giving your answer in the form , where k is an integer.` Solution a. […]