Question

Find the vertices and foci of the ellipse in the equation

Answer 1

here is the equation

Answer 2

The vertices of an ellipse, if the equation is written in the form \[\frac{ x^2 }{ a^2 }+ \frac{ y^2 }{ b^2 }=1\]
then the vertices are equal to a.
In this case a is the square root of 25, so the vertices are (5,0) and (-5,0)
To find the foci, you need to find c using\[a^2+b^2=c^2\]
So if, 25+9=c^2, then the foci are (√34,0) and (-√34,0)
Note that the foci and vertex values that I found were placed in the x-value of the coordinates because this is a horizontal ellipse. This is a horizontal ellipse because the number under x is greater than the number under y.

Answer 3

thank you so much @trainwrecking this was very helpful

Answer 4

No problem! :)

Answer 5

@trainwrecking sorry for bothering, but I totally got what you explained but the answer is in the form choices , looking at them I cant tell where is the correct answer, can you help please?
these are the choices

A) foci = (-2, 0) and (2, 0); vertices = (-5, 0) and (5, -0)
B) foci = (-4, 0) and (4, 0); vertices = (0, 3) and (0, -3)
C) foci = (-4, 0) and (4, 0); vertices = (-5, 0) and (5, -0)
D) foci = (4, 4) and (0, 0); vertices = (-5, 0) and (5, -0)

Answer 6

Oh, that was my mistake! To find the foci, you should actually use \[a^2-b^2=c^2\] So the foci would actually be (4,0) and (-4,0) and the correct answer choice is C. SO sorry about that!

Answer 7

ok so that is the equation, got it .

dont be , I appreciate your help. thank you so much @trainwrecking