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📐 Mathematics  ·  Straight Lines  ·  JEE

The equation of director circle of ellipse x²/a² + y²/b² = 1 is:

Answer: x² + y² = a² + b².

  • A x² + y² = a² + b²
  • B x² + y² = a² - b²
  • C x² + y² = a² × b²
  • D x² + y² = 2ab

Correct answer: A. x² + y² = a² + b²

Explanation: Director circle is locus of points from which the two tangents to ellipse are perpendicular. Its equation: x² + y² = a² + b².

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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