Which of the following equations belongs to an ellipse with vertical orientation?

a. 16x^2 +25 y^2 = 1
b. x^2 - 16 y^2 = 1
c. x^2/16-y^2/25=1
d. 16x^2 +y^2 = 16
e. x^2 + 16y^2 = 16
f. none of these.

d. 16x² + y² = 16

Step-by-step explanation:

Standard form of an ellipse is:

x² / a² + y² / b² = 1

If b > a, the ellipse has a vertical orientation.

We can ignore options b and c, since they have minus signs in them.

Convert the other options to standard form:

a. x² / (1/16) + y² / (1/25) = 1

x² / (1/4)² + y² / (1/5)² = 1

1/4 > 1/5

d. x² + y² / 16 = 1

x² / 1² + y² / 4² = 1

1 < 4

e. x² / 16 + y² = 1

x² / 4² + y² / 1² = 1

4 > 1

Of these three options, only d is a vertical ellipse.

step-by-step explanation: it is d