AP EAMCET · Maths · Ellipse

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 $C P$ is

A $25$
B $9$
C $4$
D $5$

Verified Solution

Answer & Solution

Correct Answer

(B) $9$

Step-by-step Solution

Detailed explanation

Given equation of ellipse is x225+y216=1. Here a=5, b=4 and the centre of the ellipse is (0,0). The major axis of ellipse is along the X-axis and minor axis is along Y-axis. The distance of point P(x,y) from the centre of the ellipse C is maximum, only when the point P(x,y)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If a point Px,y moves along the ellipse x225+y216=1 and if C is the centre of the ellipse, then the sum of maximum and minimum values of CP is

Step-by-step Solution

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 $C P$ is