Question

Find the standard form of the equation of the ellipse with the given characteristics

vertices: (-9, -11) (-9,7) minor axis of length: 16

Answer 1

I got (x+9)^2/81+(y+2)^2/64=1
Is that right?

Answer 2

well, look at the vertices locations => (-9, -11) (-9,7)
notice the "x" coordinate doesn't change
the "y" coordinate does

that means the ellipse major axis is vertical
so, what's the distance between -11 and +7? well, 18, half that is "a"
a = 9

the "b" component is given, minor axis is 16, half that is "b"
b = 8

now the center of the ellipse is half-way between the 2 vertices
so what's the midpoint of (-9, -11) (-9,7) ?
well x = -9
from -11 going up "a" units, or 9 units, then -11+9 = 2

so the center is at (-9, 2)

Answer 3

am i right though? I knew all that its always the center that gets me

Answer 4

the center is half-way through the vertices, you can always just use the "midpoint equation" for that, so you have in this case 2 points

Answer 5

I just noticed using the midpoint formula, center should be (-9, -2) dohhh
-11 up 9 units, lands still on the 3rd quadrant heheh

Answer 6

you can always just use the "midpoint equation" for that, so you have in this case 2 points
$$
(-9, -11) (-9,7)\\
\left(\cfrac{x_2 + x_1}{2},\cfrac{y_2 + y_1}{2} \right)\\
\left(\cfrac{-9 + (-9)}{2},\cfrac{7 + (-11)}{2} \right)\\
\left(-9,-2 \right)
$$