Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2).

Question

tkhunny · Answer

It's an ellipse.  It looks like this: $\dfrac{(x-h)^{2}}{a^{2}}+\dfrac{(y-k)^{2}}{b^{2}} = 1$

Looking at all the vertices, it is apparent that the center is (0,0).

$\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}} = 1$

Looking at (10,0) and (-10,0), then a = 10

$\dfrac{x^{2}}{10^{2}}+\dfrac{y^{2}}{b^{2}} = 1$

Looking at (0,2) and (0,-2), then b = 2

$\dfrac{x^{2}}{10^{2}}+\dfrac{y^{2}}{2^{2}} = 1$

One for free.  You show us another one.

katherinesmith · Answer

goodness. okay hold on.

katherinesmith · Answer

well my next one is the equation of an ellipse centered at the origin with foci at (0, -3) and (0, 3) and a major axis of 10.

which is different than that one.

tkhunny · Answer

Barely different.  Go!  Follow my model or invent your own.

katherinesmith · Answer

how is it barely different! :(

tkhunny · Answer

Follow my model.  One thing at a time.

katherinesmith · Answer

how is the foci and major axis anything like your model.

tkhunny · Answer

Are you going to work on it or argue with me?  What do you know and what do you need to know?  Same thing.

tkhunny · Answer

Major axis is in the same direction as the foci.

The major axis length is twice "a".

$c^{2} = a^{2} - b^{2}$

Plenty of information.  Go!!