\( x 2..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> \( x 2..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> \( x 2..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />

Question 46

Mathematics Parabola Hard

The sum of the focal distances of any point on the ellipse&nbsp;<span class="math-tex">\(\rm \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2}=1, a&lt;b\)</span>,&nbsp;with eccentricity e, is given by:

(A) 2ae
(B) 2b
(C) 2a
(D) 2be
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Here \(a < b\), so the major axis is along the y-axis and its length is \(2b\). The foci are \((0, \pm be)\).

For any point on an ellipse, the sum of its distances from the two foci equals the length of the major axis.

Sum of focal distances = \(2b\)

Answer: (B) 2b

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