Question

Arrange the ellipses in ascending order of their eccentricities when $\angle SB{S}^1$ is given, where $S$ & $S^1$ are foci and $B$ is one end of the minor axis. For the four ellipses $A,B,C,D$ $\angle SB{S}^1={20}^0,{60}^0,{30}^0,{90}^0$

• A. A, C, B, D
• B. D, B, C, A
• C. B, D, C, A
• D. A, C, D, B

Answer 1

Answer: (A)

A, C, B, D

Eccentricity can be thought of as a measure of how much the conic section deviates from being circular.

Eccentricity for a circle is 0.

Eccentricity for an ellipse is greater than 0 but less than 1.

For an ellipse to be a circle, $S$ and $S_1$ should coincide each other which means $\angle SB{S}_1=0$.

So, as the angle between $SB{S}_1$ increases the eccentricity of the ellipse increases.