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📐 Mathematics  ·  Conic Sections  ·  JEE

Find the equation of an ellipse whose major axis is along the y-axis, with semi-major axis 5 and semi-minor axis 3.

Answer: x 2 /9 + y 2 /25 = 1.

  • A x<sup>2</sup>/9 + y<sup>2</sup>/25 = 1
  • B x<sup>2</sup>/25 + y<sup>2</sup>/9 = 1
  • C x<sup>2</sup>/9 - y<sup>2</sup>/25 = 1
  • D x<sup>2</sup>/5 + y<sup>2</sup>/3 = 1

Correct answer: A. x<sup>2</sup>/9 + y<sup>2</sup>/25 = 1

Explanation: Major axis along y-axis: standard form x²/b²+y²/a²=1 with a=5 (semi-major) and b=3 (semi-minor). So denominators: b²=9 under x², a²=25 under y². Equation: x²/9+y²/25=1. Ans: x²/9+y²/25=1.

The Four Conics by EccentricityCircle (e=0)Ellipse (0<e<1)Parabola (e=1)Hyperbola (e>1)

All four conics form a single family distinguished only by eccentricity: a circle is the most "closed" (e=0), an ellipse is an elongated closed curve, a parabola is the borderline open curve (e=1), and a hyperbola has two separate open branches (e>1).

Concept context

Study circles, parabolas, ellipses, and hyperbolas as curves formed by intersecting a plane with a double cone, with their standard equations and key properties.

Read the full Conic Sections notes →