Question

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

• A. $25$
• B. $9$
• C. $4$
• D. $5$
• E. $16$

Answer 1

The correct option is B

$9$

Step 1: Expressing the given data:

Given ellipse is ${\text{(x}}^2{\text{/ 16) + (y}}^2\text{/ 25) = 1}$

On comparing with the ellipse equation ${\text{(x}}^2{{\text{/ a}}^2}^{{}^{}}{\text{) + (y}}^2{\text{/ b}}^2\text{) = 1}$

we get, $a^2=16,b^2=25$

$\therefore a=4$ and $\text{b = 5}$

Step 2. Maximum and minimum values of $\mathbf{\text{CP}}$

$\text{CP}$ is maximum when $\text{P}$ is at the end of the major axis.

Maximum value of $\text{(CP)}$$=5$

Similarly, $\text{CP}$is minimum when $\text{P}$ is at the end of the minor axis.

Minimum value of $\text{(CP)}$= 4

Step 3. Sum of Maximum and minimum values of $\mathbf{\text{CP}}$

The sum of maximum and minimum values of $\left(\mathrm{CP}\right)\text{= 5 + 4 = 9}$

Hence, option $\mathbf{\text{"B"}}$ is correct.