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The equation of tangent to ellipse x²/a² + y²/b² = 1 with slope m is:

Answer: y = mx ± √(a²m²+b²).

  • A y = mx ± √(a²m²+b²)
  • B y = mx ± √(a²-b²)
  • C y = mx + c
  • D y = mx ± ab

Correct answer: A. y = mx ± √(a²m²+b²)

Explanation: Substitute y=mx+c into ellipse; discriminant=0 gives tangency condition: c²=a²m²+b². So c=±√(a²m²+b²), and tangent is y=mx±√(a²m²+b²). Ans: y=mx±√(a²m²+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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