If a point P x - y moves along the ellipse x 2-25- y 2-16-1 and if C is the centre of the ellipse- then- 4 max CP -5 min CP -A- 30B- 40C- 45D- 25

The correct option is B 40 Given ellipse is x^2/25+y^2/16=1 Here, a =5 and b =4 MaxCP is the maximum distance from the centre to a point on the ellipse. It is ...

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Byju's Answer

Standard XI

Mathematics

Terminologies Related to an Ellipse

If a point P ...

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

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Solution

The correct option is C
40

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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Similar questions

Q. If a point

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and if

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Q. If the line

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If a point P(x,y) moves along the ellipse x225+y216=1 and if C is the centre of the ellipse, then, 4 max{CP} + 5 min{CP}=___ .

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}=___ .