question_answer

If a point\[P(x,\text{ }y)\]moves along the ellipse \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\]and if C is the centre of the ellipse, then the sum of maximum and minimum values of CP is

A)  25         

B)                         9

C)  4                            

D)         5

E)  16

Correct Answer: B

Solution :

The given equation of ellipse is \[\frac{{{x}^{2}}}{25}+\frac{{{y}^{2}}}{16}=1\] Comparing it with                 \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] \[\Rightarrow \]               \[a=5,b=4\] and      centre of ellipse = (0, 0) \[\therefore \]Maximum distance of CP                 \[=\sqrt{{{(5-0)}^{2}}+{{(0-0)}^{2}}}=5\] and minimum distance of CP                 \[=\sqrt{{{(0-0)}^{2}}+{{(4-0)}^{2}}}=4\] \[\therefore \]  Sum \[=5+4=9\]