(a).

Number of test aircrafts is .

According to data collected from first test aircraft, it was kilometers farther from Airport  than Airport .

The two airports are kilometers apart along the same highway, with Airport due south of Airport .

Distance between airports is kms.

The absolute value of the difference of the distances from any point on a hyperbola to the foci is .

The two airports are foci of the hyperbola and kilometers apart.

For hyperbola :

Airport due south of Airport so the transverse axis is vertical.

The transverse axis is vertical and the center of the hyperbola is located at the origin so the term goes with the term and the equation will be .

Substitute and in the hyperbola equation. \ \

(b).

Graph :

(1).Draw the coordinate plane.

(2).Graph the equation .

Observe the graph :

The plane is on top branch because it is closer to the Airport A.

(c).

The highway is transverse axis and the plane is kms away from the highway.

.

Subustiute in the equation .

.

Therefore the coordinates of the plane are .

(a). The equation is .

(b).  Graph of the equation is \ \

\ \

The plane is on top branch because it is closer to the Airport A.

(c). Coordinates of the plane are .