Question

GUYS PLS. HELP. find the equation of ellipse. center @origin.
focus at (- square root 13, 0) vertex at (0,2).

Answer 1

With focus at \((-\sqrt {13},0)\) and a vertex at \((0,2)\), we have the following situation:
Equation of an ellipse is \(\large {x^2 \over a^2}+{y^2\over a^2-f^2}=1\), where a=half the major axis (horizontal) and f is the focus. We are given that b, half the minor axis is 2.

Focus: \(f=\sqrt{a^2-b^2}\), from which we can get a.

We now have everything we need to solve this problem.

Does this make sense?

Answer 2

yes yes thank you :)))

Answer 3

your welcome

Answer 4

@ybarrap how did you come up with 9 (in the graph) ? i mean, square root of 13 equal to 3.60.. hehe

Answer 5

In the graph, it's actually an "a" not a "9". That's the x-coordinate of the vertex for one on the the major axis of the ellipse, (a,0).

Answer 6

the sqrt of 13 is the focus and is not on the vertex, but located a short distance before it.

Answer 7

does this make any sense, i know my sketching is terrible

Answer 8

sorry hahaha. yes thank you again ;)

Answer 9

not a problem