Question

When an airplane flies faster than the speed of sound, it produces a shock wave in the shape of a cone. Suppose the shock wave intersects the ground in a curve that can be modeled by x^2-14x+4= 9y^2-36y Identify the shape of the curve.

a. circle
c. ellipse
b. hyperbola
d. parabola

Answer 1

(b) hyperbola

Explanation:

The x- and y-terms are both squared. When written in standard form, they have opposite signs. That means the equation describes a hyperbola.

x^2 -14x +4 = 9y^2 -36y . . . . . given

x^2 -14x +4 -9y^2 +36y = 0 . . . . subtract right side

x^2 -14x +49 -9(y^2 -4y +4) = 45 -36 . . . . complete the squares

(x -7)^2 -9(y -2)^2 = 9 . . . . . . write as squares

(x -7)^2/9 -(y -2)^2 = 1 . . . . . . standard form equation for hyperbola