A drone's horizontal distance d d\,d and vertical height h h\,h from a tracking station are modeled by the parametric equations
d=2t+54t−1,h=144t−1,t>0.25 d = \frac{2t + 5}{4t - 1}, \quad h = \frac{14}{4t - 1}, \quad t > 0.25 d=4t−12t+5,h=4t−114,t>0.25where t t\,t is the time in minutes after launch.
Show that the path of the drone lies on a straight line.
Hence, or otherwise, determine the horizontal distance d d\,d of the point where the drone's path intersects a boundary defined by the line h=3d−5h = 3d - 5h=3d−5.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.