Which of the following equations represents a parabola with a horizontal axis of symmetry, vertex at (-7, 12), and p = -6?

A. (x - 12)² = -24(y + 7)

B. (y - 12)² = -24(x + 7)

C. (x + 12)² = 24(y - 7)

D. (y + 12)² = 24(x - 7)

An elliptical mirror measures 20 inches wide and 24 inches high. The ellipse is centered at (0, 60) on a coordinate plane, where units are in inches. Which equation represents the mirror?

A. x^2/144 + (y-60)^2/100 = 1

B. x^2/576 + (y-60)^2/400 = 1

C. (y-60)^2/144 + x^2/100 = 1

D. (y-60)^2/576 + x^2/400 = 1

The hyperbolic orbit of a comet is represented on a coordinate plane with center at (0, 6). One branch has a vertex at (0, 14) and its respective focus at (0, 16). Which equation represents the comet's orbit?

A. (y-6)^2/100 - x^2/64 = 1

B. (y-6)^2/64 - x^2/36 = 1

C. x^2/100 - (y-6)^2/64 = 1

D. x^2/36 - (y-6)^2/64 = 1

An elliptical-shaped path surrounds a garden, modeled by(x-20)^2/169+ (y-18)^2/289 = 1, where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?

A. 169 feet; minor axis

B. 34 feet; major axis

C. 17 feet; major axis

D. 13 feet; minor axis

A vase can be modeled using x^2/6.25 - (y-4)^2/42.25 = 1 and the x-axis, for 0y20, where the measurements are in inches. Using the graph, what is the distance across the base of the vase, and how does it relate to the hyperbola?

A. 2.25 inches; length of the transverse axis

B. 2.94 inches; distance between the intercepts

C. 4.50 inches; length of the transverse axis

D. 5.87 inches; distance between the x-intercepts