Conic Sections Story Problem?

Question

I can't figure out which type of conic section (parabola, ellipse, or hyperbola) this question is asking for. Any help would be greatly appreciated!

A wagon train heading west is traveling 20 miles each day in a particular terrain. A scout sets out in the morning to check out possible routes ahead or ride in other directions looking for danger. The scout can travel up to 40 miles before returning to the wagon train by sundown. Sketch the region the scout can survey as the wagon train travels along the x-axis. Then write an inequality that describes this region.

Thank you again for your help!!

Answer 1

You are looking for an ellipse. The inside of the ellipse would be the area that the scout could survey. 20 would be the distance between the foci and 40 would be the vertices. Good Luck

Answer 2

you ought to complete the sq. one after the different for the x and y aspects, so first rearrange to positioned the x's and y's mutually. 16x^2 + 64x + 9y^2 - 18y - seventy one = 0 16(x^2 + 4x) + 9(y^2 - 2y) - seventy one = 0 16(x^2 + 4x + 4 - 4) + 9(y^2 - 2y + a million - a million) - seventy one = 0 16(x^2 + 4x + 4) - sixty 4 + 9(y^2 - 2y + a million) - 9 - seventy one = 0 16(x+2)^2 + 9(y+a million)^2 - one hundred and forty four = 0 This equation is placing out to appear like an ellipse. 16(x+2)^2 + 9(y+a million)^2 = one hundred and forty four (x+2)^2 / 9 + (y+a million)^2 / 16 = a million (x+2)^2 / 3^2 + (y+a million)^2 / 4^2 = a million The equation is an ellipse with a important axis of four instruments vertically, and a minor axis of three instruments horizontally, dependent at (-2,-a million).

Answer 3

what grade is this ill see if i can get my mom's help but if not good luck! it might be a parabola i think but....