Question

40 points!!
What's the equation for this ellipse?

Answer 1

The answer to your question is
`((x + 5)^(2) )/(4) + ((y + 8)^(2) )/(36) = 1`

Explanation:

From the graph we know that the center = (-5, -8) and a= 6 and b = 2.

See the picture below

Here, we have a vertical ellipse so the equation is

`((x - h)^(2) )/(b^(2) ) + ((y - k)^(2) )/(a^(2) ) = 1`

Substitution

`((x + 5)^(2) )/(2^(2) ) + ((y + 8)^(2) )/(6^(2) ) = 1`

`((x + 5)^(2) )/(4) + ((y + 8)^(2) )/(36) = 1`

Answer 2

(x +5)²/4 +(y +8)²/36 = 1

Explanation:

The equation of an ellipse with center (h, k) and semi-axes "a" and "b" (where "a" is in the x-direction and "b" is in the y-direction) can be written as ...

((x -h)/a)² +((y -k)/b)² = 1

Here, the center is at (h, k) = (-5, -8), and the semi-minor axis is a=2, while the semi-major axis is b=6.

The equation can be written as ...

((x +5)/2)² +((y +8)/6)² = 1

More conventionally, it is written ...

(x +5)²/4 +(y +8)²/36 = 1