A hyperbola has its foci at (7, 5) and (7, −5). A directrix of the hyperbola is y = . What is the equation of the hyperbola? = 1 = 1 = 1 = 1

y²/16 − (x − 7)²/9 = 1

Step-by-step explanation:

Assuming the directrix is y = 16/5.

The distance between the directrix and the center is a²/c, where a is the distance from the center to the vertex and c is the distance from the center to the focus.

The center is the midpoint between the foci: (7, 0).  So c = 5.

The distance between the directrix and the center is 16/5.  Solving for a:

a²/5 = 16/5

a² = 16

a = 4

The equation of a vertical hyperbola is:

(y − k)²/a² − (x − h)²/b² = 1

where (h, k) is the center,

a is the distance to the vertices,

and b² = c² − a².

In this case, (h, k) is (7, 0), a² = 4² = 16, and b² = 5² − 4² = 9.

y²/16 − (x − 7)²/9 = 1

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

probably .5

i can on others if necessary.