Question

Identify coordinates of the four vertices of
(x+2)^2/9 + (y-3)^2/16 =1

Answer 1

This is a vertical ellipse of the form:

\( \Large
\frac {(x-h)^2}{b^2} + \frac {(y-k)^2}{a^2} = 1
\)

Compare the general equation above to the given equation and identify: a, b, h, k;
where (h,k) is the center of the ellipse and 'a' is the semi-major axis and 'b' is the semi-minor axis. Knowing a, b, h, k, you can determine the coordinates of all four vertices.

Answer 2

So they would be 4,3,-2,3? @aum

Answer 3

You have to say which is which.
a = 4, b = 3, h = -2, k = 3

The center is (h,k) which is (-2,3).
The top vertex will be at a height "a" ABOVE the center. That means, the y-coordinate will be 4 units above the center but the x-coordinate will be the same as the center.
Top Vertex at (-2, 3+4) = (-2,7).

Can you find the other three vertices?

Answer 4

(-2,-1)?

Answer 5

I'm not sure about the other 2

Answer 6

Yes, the bottom vertex is (-2,-1).

What is the left vertex? Notice how the left and right vertices are at the same height as the center which means their y-coordinates will be the same as that of the center. Only the x-coordinates will decrease by "b" units or "3 units" for the left vertex and increase by "3 units for the right vertex.

Answer 7

oh, so they're (1,3) and (-5,3)?

Answer 8

Yes.

Answer 9

thank you :]

Answer 10

You are welcome.