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
