Question

What are the coordinates of the center of the ellipse shown below?


`((x-7)^2)/(4) + ((y+3)^2)/(16) = 1`

A. (-7,3)
B. (4,16)
C. (2,4)
D. (7,-3)

Answer 1

Option D (7, -3)

Explanation:

We know that the general equation of an ellipse has the form:

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

Where the point (h, k) are the coordinates of the center of the ellipse

In this case the equation of the ellipse is:

`((x-7)^2)/(4) + ((y+3)^2)/(16) = 1`

Then

`h=7\\\\k = -3`

So The coordinates of the center of the ellipse are (7, -3)

Answer 2

D. (7,-3)

Explanation:

This equation is for vertical Ellipse;

For vertical Ellipse;

• center of ellipse is given by (h,v)
• vertices for ellipse is given by (h, v ± a)
• co-vertices for the ellipse is given by (h ±b, v)

where the equation is (x-h)²/b² + (y-v)²/a²

In this question;

h=7 and v= -3

center= (7,-3)