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📐 Mathematics  ·  Straight Lines  ·  JEE

Centres of two circles are (0,0) and (5,0). Radii are 3 and 2. Circles are:

Answer: Externally tangent.

  • A Externally tangent
  • B Internally tangent
  • C Intersecting at two points
  • D Non-intersecting

Correct answer: A. Externally tangent

Explanation: Distance between centres d=√(5²+0²)=5. Sum of radii r₁+r₂=3+2=5. Since d=r₁+r₂ exactly, the circles touch at exactly one external point. Ans: Externally tangent.

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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