Question

applying parabolas to a satellite dish. the shape of a satellite dish can be described as parabolic. satellite dishes are this shape because radio waves are reflected from the surface of the dish and received into the focus. if the graph of the satellite dish is given by the equation x² = 8y, what are the coordinates of the focus?

Explanation:

Step1: Recall the standard - form of parabola equation

The standard - form of a parabola opening upwards is $x^{2}=4py$.

Step2: Compare with the given equation

Given $x^{2}=8y$, comparing with $x^{2}=4py$, we have $4p = 8$.

Step3: Solve for $p$

Dividing both sides of $4p = 8$ by 4, we get $p=\frac{8}{4}=2$.

Step4: Find the focus coordinates

For a parabola $x^{2}=4py$ opening upwards with vertex at the origin $(0,0)$, the focus is at the point $(0,p)$. Since $p = 2$, the focus is at $(0,2)$.

Answer:

$(0,2)$