Question

The equation (x-7^2/64)+(y+2)^2/9=1 represents an ellipse.

Answer 1

Answer:

D aka (15,-2) and (-1,-2)

Step-by-step explanation:

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Answer 2

Answer:

Vertices of the ellipse are, (15, -2) and (-1, -2)

Step-by-step explanation:

The equation of the ellipse is,

$\dfrac{\left(x-7\right)^2}{64}+\dfrac{\left(y+2\right)^2}{9}=1$

The general equation of ellipse with centre as (h, k) is,

$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$

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,

$=(h\pm a,k)$

So, vertices of the given ellipse are,

$=(7+8,-2),(7-8,-2)\\\\=(15,-2),(-1,-2)$