Question

rene is designing a satellite that is the shape of a parabola that opens upward with a diameter of 8 in. and a depth of 2 in. the feed antenna focuses the incoming radio waves. at what point should the feed antenna be placed? (-8, 0) (-2, 0) (0, 2) (0, 8)

Explanation:

Step1: Set up the parabola equation

The standard - form equation of a parabola opening upward with vertex at the origin is $x^{2}=4py$. Since the diameter is 8 in. and depth is 2 in., when $x = 4$ (half of the diameter), $y = 2$.

Step2: Find the value of $p$

Substitute $x = 4$ and $y = 2$ into $x^{2}=4py$. We get $4^{2}=4p\times2$. Simplify the left - hand side: $16 = 8p$. Solve for $p$ by dividing both sides by 8, so $p = 2$.

Step3: Determine the focus

For a parabola of the form $x^{2}=4py$ opening upward, the focus is at the point $(0,p)$. Since $p = 2$, the focus is at $(0,2)$.

Answer:

C. $(0,2)$