A research drone is programmed to follow a specific surveillance path during a flight test. Its position (x,y)(x, y)(x,y) in kilometers relative to a base station at time t t\,t is given by the parametric equations
x=4sectandy=7tantwhere 0≤t<π2 x = 4\sec t \quad \text{and} \quad y = 7\tan t \quad \text{where } 0 \le t < \frac{\pi}{2} x=4sectandy=7tantwhere 0≤t<2πWhich of the options shown below is a Cartesian equation for the drone's path?
x216+y249=1\frac{x^2}{16} + \frac{y^2}{49} = 116x2+49y2=1
49x2−16y2=78449x^2 - 16y^2 = 78449x2−16y2=784
16x2−49y2=78416x^2 - 49y^2 = 78416x2−49y2=784
x2−y2=33x^2 - y^2 = 33x2−y2=33
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.