Question

Arrange the following conics in ascending order on the basis of their eccentricity values.

Answer 1

As we know that,
$\text{e}=\frac{PS}{PM}$
Where, PS is distance from fixed point and PM is distance from fixed line.
$1.$ For circle PM is equal to infinity. So, the ratio will be zero which concludes e = 0.
$2.$ For ellipse PS is less than PM. So, the ratio will be less than $1.$ which concludes e < 1.
$3.$ For parabola PS is equal to PM. So, the ratio will be equal to $1.$ which concludes e = 1.
$4.$ For hyperbola PS is greater than PM. So, the ratio will be greater than $1.$ which concludes e > 1.