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.

The answer to this question is D

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.