Question

Identify the ellipses, represented by equations, whose eccentricities are less than 0.5

Answer 1

Answer:

1, 4 and 6 for plato

Step-by-step explanation:

Answer 2

Answer:

See explanation

Step-by-step explanation:

Hello, we cannot see the ellipse equations.

The eccentric of an ellipse is given by:

$e = \frac{c}{a}$

Assuming the equations are:

$\frac{ {x}^{2} }{25} + \frac{ {y}^{2} }{16} = 1$

Then a²=25 and b²=16

${c}^{2} = {a}^{2} - {b}^{2}$

${c}^{2} = 25 - 16$

${c}^{2} = {3}^{2}$

$c = 3$

The eccentricity is:

$e = \frac{3}{5} = 0.6$

If the ellipse has equation,

$\frac{ {x}^{2} }{ {5}^{2} } + \frac{ {y}^{2} }{ {3}^{2} } = 1$

then the this time, we have a=5 and b=3.

This means that:

${c}^{2} = {a}^{2} - {b}^{2}$

${c}^{2} = {5}^{2} - {3}^{2}$

${c}^{2} = {4}^{2}$

$c = 4$

$c = \frac{4}{5} = 0.8$