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COMEDK · Maths · 14. Ellipse

If the two ends of the major axis of an ellipse are \((5, 0)\) and \((-5, 0)\) and one focus lies on the line \(3x - 5y - 9 = 0\), then its equation is

  1. A \(\dfrac{x^2}{25} + \dfrac{y^2}{9} = 1\)
  2. B \(\dfrac{x^2}{16} + \dfrac{y^2}{25} = 1\)
  3. C \(\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1\)
  4. D \(\dfrac{x^2}{25} + \dfrac{y^2}{34} = 1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1\)

Step-by-step Solution

Detailed explanation

The ends of the major axis are given as \((5, 0)\) and \((-5, 0)\). This implies that the center of the ellipse is at the origin \((0, 0)\) and the semi-major axis is \(a = 5\). The foci of the ellipse lie on the major axis, which is the x-axis. Thus, the coordinates of the foci…