Question

matteo is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. the shape of his satellite can be modeled by ( y^{2}=6x ) where ( x ) and ( y ) are modeled in inches. he realizes that the static is a result of the feed antenna shifting slightly off the focus point. what is the focus point of the satellite?
( (-1.5,0) )
( (0,-1.5) )
( (0,1.5) )
( (1.5,0) )

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens to the right or left is \(y^{2}=4px\).

Step2: Compare the given equation with the standard form

Given \(y^{2}=6x\), comparing with \(y^{2}=4px\), we have \(4p = 6\).

Step3: Solve for \(p\)

$$
LATEXBLOCK0
$$

Step4: Determine the focus point

For a parabola \(y^{2}=4px\) that opens to the right (since \(p>0\) here), the focus is at \((p,0)\). Substituting \(p = 1.5\), the focus is \((1.5,0)\).

Answer:

\((1.5,0)\)