A punter in football punts a ball, and it follows the path set by the equation y = -1/2(x - 35)^2 + 75. Which of the conic sections does the path of the football take?

Question

whpalmer4 · Answer

Are you sure you have the equation correct?  at x = 0, that football is pretty far underground!

anonymous · Answer

yes, thats what is written on my homework..

whpalmer4 · Answer

Well, no matter, you aren't being asked to evaluate it.

General equation for a conic section is

$$Ax^2 + Bxy + Cy^2+ Dx + Ey + F = 0$$Expand yours and compare the terms you get.  You can identify the form of conic section you have from the value of $B^2-4AC$:

$B^2-4AC < 0$ either ellipse or circle
$B^2-4AC = 0$ parabola
$B^2-4AC > 0$ hyperbola