Question The line meets the the curve at the points A and B as shown in the figure. a. Find the coordinates of A and the coordinates of B. b. Find the distance AB in the form where r is a rational number. Solution a. We are required to find the coordinates of the points […]
Question The line has equation 4x + 2y – 3 = 0. a. Find the gradient of . The line is perpendicular to and passes through the point (2,5). b. Find an equation of in the form y = mx + +c, where m and c are constants. Solution a. We are given equation of line ; We are […]
Question Figure shows a sketch of the curve H with equation; , a. Give the coordinates of the point where H crosses the x-axis. b. Give the equations of the asymptotes to H. c. Find an equation for the normal to H at the point P(–3, 3). This normal crosses the x-axis at A […]
Question Figure 1 shows a sketch of the curve with equation y = f(x) where , The curve crosses the x-axis at (1, 0), touches it at (–3, 0) and crosses the y-axis at (0, –9). a. In the space below, sketch the curve C with equation y=f(x+2) and state the coordinates of the points where the […]
Question The straight line L1 passes through the points (–1, 3) and (11, 12). a. Find an equation for L1 in the form ax + by + c = 0, where a, b and c are integers. The line L2 has equation 3y + 4x – 30 = 0. b. Find the coordinates of the point of intersection […]
Question The curve C has equation , a. Find , giving each term in its simplest form. The point P on C has x-coordinate equal to . b. Find the equation of the tangent to C at P, giving your answer in the form y = ax + b, where a and b are constants. The […]
Question Figure 1 shows a sketch of the curve with equation , x ≠ 0. The curve C has equation , x ≠ 0, and the line has equation y = 4x + 2. a. Sketch and clearly label the graphs of C and on a single diagram. On your diagram, show clearly the coordinates of the […]
Question The line L1 has equation y = -2x+3. The line L2 is perpendicular to L1 and passes through the point (5, 6). a. Find an equation for L2 in the form ax + by + c = 0, where a, b and c are integers. The line L2 crosses the x-axis at the point A and the y-axis […]