Question

identify the conic section from its equation.
(x-5)^2/4+(y+3)^2/16=1

Answer 1

this is an ellipse

Answer 2

are all the ones that look like this equation ellipses?

Answer 3

@IMStuck

Answer 4

Ok, ellipses are x^2 + y^2 over a and b=1, and the a is always bigger than the b. That tells you which vertices are the major and which are the minor. Hyperbolas are x^2 - y^2=1. Parabolas are either an x^2 or a y^2, but not both in the same equation. Do you have more of these?

Answer 5

If they look like that with an x^2 first and it is added to a Y^2, then yes, it is an ellipse.

Answer 6

yes i do um there is one that says X^2+y^2+6x-16y+48=0

Answer 7

Elliipse.

Answer 8

Nononono circle I think. Hold on just one sec!!!!

Answer 9

ok

Answer 10

yes it is a circle. I had to complete the square and get it into standard form which is:\[(x+3)^{2}+(y-8)^{2}=25\]That is a circle with center (-3,8) and a radius of 5.

Answer 11

If it was an ellipse it would HAVE to equal 1 and this one does not work out that way.

Answer 12

what about one that says y^2+6y-2x+13=0

Answer 13

Here are a couple of rules to keep in the back of your mind regarding quadratic equations:
In the second degree equation\[Ax ^{2}+By ^{2}+Cx+Dy+E=0\]j(which is the format of your equation exactly!):
1. If A=B, the equation may define a circle.
2. If A and B have the same sign and A does NOT equal B, the equation may define an ellipse.

Answer 14

Here your A=B so it cannot be an ellipse.

Answer 15

The one you just asked about has a y^2 only. That makes it a parabola in the form \[y ^{2}=4px\]

Answer 16

It opens to the right and the focus lies on the x axis and the directrix is an x= ??? line.

Answer 17

We could solve those if you need to eventually...

Answer 18

I love these things. They were SO hard for me to learn; I literally spent HOURS mastering them.

Answer 19

Anyway, enough of that! ; ) Tag me if you need me again!

Answer 20

ok thank you :D