Question

Which of the following is the equation of an ellipse centered at (5,1) having a vertical minor axis of length 4 and a major axis of length 6?
Options are in image

Answer 1

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

$\frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1$

where

• 2b = vertical axis length
• 2a = horizontal axis length

(as in the picture)

So it should be like:

$\frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1$

Since it should be moved to the right and up, the answer would be:

$\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1$