Question

Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10. (5 points)

x squared divided by 5 plus y squared divided by 8 = 1

x squared divided by 25 plus y squared divided by 64 = 1

x squared divided by 8 plus y squared divided by 5 = 1

x squared divided by 64 plus y squared divided by 25 = 1

Answer 1

Answer:

$\frac{x^2}{25}+\frac{y^2}{64}=1$

Step-by-step explanation:

If the ellipse has a vertical major axis of length 16, then

$2a=16$

$\Rightarrow a=8$

If the ellipse has the length of the minor axis to be 10, then;

$2b=10$

$\Rightarrow b=5$

The equation of the ellipse is given by;

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Thus;

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

$\frac{x^2}{25}+\frac{y^2}{64}=1$