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Question

If a point P(x,y) moves along the ellipse (x2/16)+(y2/25)=1 and C is the centre of the ellipse, then the sum of maximum and minimum values of CP is


A

25

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B

9

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C

4

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D

5

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E

16

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Solution

The correct option is B

9


Step 1: Expressing the given data:

Given ellipse is (x2/16)+(y2/25)=1

On comparing with the ellipse equation (x2/a2)+(y2/b2)=1

we get, a2=16,b2=25

∴a=4 and b=5

Step 2. Maximum and minimum values of CP

CP is maximum when P is at the end of the major axis.

Maximum value of (CP)=5

Similarly, CPis minimum when P is at the end of the minor axis.

Minimum value of (CP)= 4

Step 3. Sum of Maximum and minimum values of CP

The sum of maximum and minimum values of CP=5+4=9

Hence, option "B" is correct.


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