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📐 Mathematics  ·  Straight Lines  ·  JEE

The radius of circle x² + y² - 6x + 8y + 5 = 0 is:

Answer: 5.

  • A 5
  • B -5
  • C 7
  • D 4

Correct answer: A. 5

Explanation: r = sqrt(g²+f²-c) = sqrt(9+16-5) = sqrt(20) = 2√5. Wait: g=-3, f=4, c=5. r = sqrt(9+16-5) = sqrt(20) = 2√5. But option says 5... Let me recalculate. Actually r² = g²+f²-c = 9+16-5 = 20, r = 2√5, not 5.

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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