Answer:
Vertices of the ellipse are, (15, -2) and (-1, -2)
Step-by-step explanation:
The equation of the ellipse is,
[tex]\dfrac{\left(x-7\right)^2}{64}+\dfrac{\left(y+2\right)^2}{9}=1[/tex]
The general equation of ellipse with centre as (h, k) is,
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
Comparing the given equation with the general form, we get the centre of the given ellipse at (7, -2) and a=8, b=3
The line through the foci intersects the ellipse at two points, the vertices.
We know that the coordinates of the vertices when (a>b) are,
[tex]=(h\pm a,k)[/tex]
So, vertices of the given ellipse are,
[tex]=(7+8,-2),(7-8,-2)\\\\=(15,-2),(-1,-2)[/tex]
