Question

What are the vertices of the ellipse given by the equation (x+6)^2/4 + (y+9)^2/1=1

Answer 1

I just saw this earlier

Answer 2

I dont know the answer tho sorry :(

Answer 3

haha thanks anyways. I think i might have posted it earlier no joke but I wasnt getting any hit. Im confused

Answer 4

@Hero Help?

Answer 5

!!!

Answer 6

haha what.. ? :p @Chlorophyll Help? :p

Answer 7

I don't like people keep closing/ open their posts !!!

Answer 8

I had a different question I anted to post. sorry..

Answer 9

@Chlorophyll

Answer 10

Lol someones angry\

Answer 11

Okay, the standard form for an ellipse is \[x^2/a^2+y^2/b^2 = 1\] which is what you've got except for those pesky +6 and +9 factors. We'll pretend they aren't there for the moment. That gives us \[x^2/4 + y^2/1 = 1\] and thus \[a^2=4\] and \[b^2=1\] which I'm confident you can solve. If a>b, the major axis of the ellipse runs horizontally, otherwise if a < b it runs vertically, and if a = b, you've got a special case of an ellipse known as a circle!

So, now we know that our ellipse has a horizontal major axis. We can set y = 0 to find the values of x which mark the points at which the ellipse crosses the x-axis. \[x^2/4 + 0^2/1 = 1\] has two solutions: x = 2 and x = -2. Now, we have to adjust the values we got because our real ellipse has those offsets which move the center point of the ellipse off of (0,0). The rightmost vertice we found was at (2,0) and the leftmost one at (-2,0). After we shift the x-values by -6 (to account for the +6 in the original equation) we get x values of 2-6 = -4 and -2-6 = -8. Then we shift our y-values by -9 (accounting for the +9) and get 0-9=-9 and 0-9=-9. That leaves our vertices at (-4,-9) and (-8,-9). As a quick check, plug those values into the original equation and verify that they are indeed points on the ellipse! (-8+6)^2/4+(-9+9)^2/1=1 and (-4+6)^2/4+(-9+9)^2/1=1 so our answer makes sense.

If we had an ellipse where the major axis was vertical, we would do the same thing except look for the values of y where x = 0.