(04.04 MC)

A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?

y = x^2/ 60 + 15

=>( x - h)^2 = 4a[ (x^2/6 + 15) - k ].

Step-by-step explanation:

Okay, in order to solve this question very well, one thing we must keep at the back of our mind is that the representation for the equation of a parabola is given as ; y = ax^2 + bx + c.

That is to say; y = ax^2 + bx + c is the equation for a parabola. So, we should be expecting our answer to be in this form.

So, from the question above we are given that "the satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground"

We will make an assumption that the point on the ground is (0,0) and the focus is (0,30). Thus, the vertex (h,k) = (0,15).

The equation that best describes the equation of the satellite is given as;

(x - h)^2 = 4a( y - k). (1).

[Note that if (h,k) = (0,15), then, a = 15].

Hence, (x - 0)^2 = (4 × 15) (y - 15).

x^2 = 60(y - 15).

x^2 = 60y - 900.

60y = x^2 + 900.

y = x^2/ 60 + 15.

Hence, we will have;

(x - h)^2 = 4a[ (x^2/6 + 15) - k ].