Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?

x^2/12 - y^2/4 = 1

Step-by-step explanation:

As the diretrices have simetrical values of x and have y = 0, the center is located at (0,0)

The formula for the diretrices is:

x1 = -a/e and x2 = a/e

And the foci is located at (a*e, 0) and (-a*e, 0)

So we have that:

a/e = 3

a*e = 4

From the first equation, we have a = 3e. Using this in the second equation, we have:

3e*e = 4

e^2 = 4/3

e = 1.1547

Now finding the value of a, we have:

a = 3*1.1547 = 3.4641

Now, as we have that b^2 = a^2*(e^2 - 1), we can find the value of b:

b^2 = 3.4641^2 * (1.1547^2 - 1) = 4

b = 2

So the equation of the hyperbola (with vertical diretrices and center in (0,0)) is:

x^2/a^2 - y^2/b^2  = 1

x^2/12 - y^2/4 = 1

50.6

step-by-step explanation:

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584