Question

If a point $P(x,y)$ 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
$=5+4=9$