If a point P(x,y) moves along the ellipse x225+y216=1 and if C is the centre o

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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, 4 max{CP} + 5 min{CP}=___ .

Options:

A . 25

B . 30

C . 40

D . 45

Answer: Option C
:
C

Given ellipse is $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$
Here, a =5 and b =4
Max{CP} is the maximum distance from the centre to a point on the ellipse. It is equal to the length of the semi-major axis (a).
Similarly, Min {CP} is equal to the length of the semi-minor axis (b).

4 max{CP} + 5 min{CP}= 4a+5b
$= 4 \times 5 + 5 \times 4 = 40$

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