The vertices of the given ellipse will be (2,-7) and (10,-7).
The given equation of an ellipse is:
[tex]\frac{(x-6)^2}{16} +\frac{(y+7)^2}{4} =1[/tex]......(1)
What is an ellipse?
An ellipse is a plane curve derived from a cone when the cone was sliced by a plane at an angle to the base.
The standard equation of an ellipse is given by:
[tex]\frac{(x-h)^2}{a^2} +\frac{(y-k)^2}{b^2} =1[/tex]
On comparing (1) with a standard equation of an ellipse we get
[tex]h=6\\k=-7\\a=4\\b=2[/tex]
We know the vertices of an ellipse(a>b) are (h-a,k) and (h+a,k)
So, the vertices of the given ellipse will be (2,-7) and (10,-7).
Hence, the vertices of the given ellipse will be (2,-7) and (10,-7).
To get more about ellipses visit:
https://brainly.com/question/450229
