Select the correct answer from each drop-down menu. the equation of a hyperbola is -4x2 + y2 + 16x + 12y + 16 = 0. the center of the hyperbola is (2, -, 2)(0, 0), and its vertices are (-4, 2)(2, -4)(2, 6) and (-8, 2)(2, -8)(2, -6)

Step-by-step explanation:

Rearranging the equation to standard form helps answer this question.

... -4(x^2 -4x) +(y^2 +12y) = -16 . . . subtract the constant, group x-terms, y-terms

... -4(x^2 -4x +4) +(y^2 +12y +36) = -16 -4(4) +36

... -4(x -2)^2 +(y +6)^2 = 4 . . . . write as squares

... ((y +6)/2)^2 -(x -2)^2 = 1 . . . . divide by 4

Now, this is in the form ...

... ((y -k)/a)^2 -((x -h)/b)^2 = 1

which has center (h, k) and vertices (h, k±a).

This form tells you the center is (x, y) = (2, -6), and the vertices are (2, -4) and (2, -8).

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have