NDA 2025 Maths · Mathematics · Conic Sections · easy

The sum of the focal distances of any point on an ellipse is constant. 2. The absolute difference of the focal distances of any point on a hyperbola…

Single correct option

Consider the following statements:
1. The sum of the focal distances of any point on an ellipse is constant.
2. The absolute difference of the focal distances of any point on a hyperbola is constant.
Which of the statements given above is/are correct?

A. $1$ only
B. $2$ only
C. Both $1$ and $2$
D. Neither $1$ nor $2$

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Answer: (C) Both $1$ and $2$

Both are the defining focal properties: for an ellipse

PF_1+PF_2=2a

, and for a hyperbola

|PF_1-PF_2|=2a

. A common slip is to swap them, remembering the sum for the hyperbola. Hence both statements are correct.

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