Question

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

Answer 1

Answer: (B)

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 $