Question Given that ,, a) Express in the form , where a and b are integers. The curve C with equation y = f(x), , meets the y-axis at P and has a minimum point at Q. b) In the space provided on page 19, sketch the graph of C, showing the coordinates of P and Q. The […]
Question The gradient of the curve C is given by The point P(1,4) lies on C. a) Find an equation of the normal to C at P. b) Find an equation for the curve C in the form . c) Using , show that there is no point on C which the tangent is […]
Question The points A(1,7), B(20,7) and C(p,q) form the vertices of a triangle ABC, as shown in Figure 2. The point D(8, 2) is the mid-point of AC. a) Find the value of p and the value of q. The line l, which passes through D and is perpendicular to AC, intersects AB at E. b) Find […]
Question The curve C has equation , . The point P on C has x-coordinate 1. a) Show that the value of at P is 3. b) Find an equation of the tangent to C at P. This tangent meets the x-axis at the point (k,0). c) Find the value of k. Solution a) We need […]
Question The curve C has equation . The point P has coordinates (3, 0). a) Show that P lies on C. b) Find the equation of the tangent to C at P, giving your answer in the form y=mx+c, where m and c are constants. Another point Q also lies on C. The tangent to C […]
Question The line passes through the point (9, – 4) and has gradient . a) Find an equation for in the form ax+by+c=0, where a, b and c are integers. The line passes through the origin O and has gradient –2. The lines and intersect at the point P. b) Calculate the coordinates of P. Given that […]