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Mathematics · JEE | CONIC SECTIONS

हिन्दी

Find the equation of the ellipse whose length of the major axis is 20 and foci are \( (0, \pm 5) \).

  1. A
    \( \frac{x^2}{100} + \frac{y^2}{75} = 1 \)
  2. B
    \( \frac{x^2}{75} + \frac{y^2}{100} = 1 \)
  3. C
    \( \frac{x^2}{25} + \frac{y^2}{100} = 1 \)
  4. D
    \( \frac{x^2}{100} + \frac{y^2}{25} = 1 \)
View Answer & Solution

Correct answer · Option B

\( \frac{x^2}{75} + \frac{y^2}{100} = 1 \)

Explanation

Length of major axis \( 2a = 20 \implies a = 10 \). Foci on y-axis gives \( c = 5 \), so \( b^2 = a^2 - c^2 = 100 - 25 = 75 \). Equation is \( \frac{x^2}{75} + \frac{y^2}{100} = 1 \).
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