Question

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

Answer 1

Answer:

  (x +5)²/4 +(y +8)²/36 = 1

Step-by-step 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

Answer 2

Answer:

The answer to your question is  $\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1$

Step-by-step 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

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

Substitution

                $\frac{(x + 5)^{2} }{2^{2} } + \frac{(y + 8)^{2} }{6^{2} } = 1$

                $\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1$