A) Increases with increase in \[\lambda \]
B) Decreases with increase in \[\lambda \]
C) Does not change with \[\lambda \]
D) None of these
Correct Answer: B
Solution :
[b] Equation of the given conic is an equation of ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}+\lambda }+\frac{{{y}^{2}}}{{{b}^{2}}+\lambda }(x\ge 0)\] \[\Rightarrow {{A}^{2}}={{a}^{2}}+\lambda \] and \[{{B}^{2}}={{b}^{2}}+\lambda \] Eccentricity, \[e=\sqrt{1-\frac{{{B}^{2}}}{{{A}^{2}}}}=\sqrt{1-\frac{{{b}^{2}}+\lambda }{{{a}^{2}}+\lambda }}\] \[=\sqrt{\frac{{{a}^{2}}+\lambda -{{b}^{2}}-\lambda }{{{a}^{2}}+\lambda }}\] \[=\sqrt{\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+\lambda }}\] \[\lambda \] is in the denominator so, when \[\lambda \] increases, the eccentricity decreases.
You need to login to perform this action.
You will be redirected in
3 sec
