1. Assuming a portion of the trajectory of a nuclear missile fired when plotted in the Cartesian plane follows a quadratic curve and is found to pass through the points (-1, 0), (0, 1) and (1, 4). A stealth plane must intercept the missile by firing a heat seeking missile which will travel in an orthogonal trajectory with the nuke. If the interception is a success at the point (2, 9), determine the equation of the trajectory of the heat seeking missile. Sketch the trajectories of both missiles.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.