2. Determine la ecuación de la hipérbola que satisface las condiciones dadas: a) Focos en (0, EV10) y un vértice en (0,3)
b) Focos en (0, +5V5) y pasa por (4, -1115)
c) Vértices en (-7,-2), (-7,-14) y una asíntota con pendiente
2

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c