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📐 Mathematics  ·  Straight Lines  ·  JEE

The combined equation of lines joining origin to intersection of y = mx + c and x² + y² = a² is:

Answer: x² + y² - a²(mx+c)²/c² = 0.

  • A x² + y² - a²(mx+c)²/c² = 0
  • B x² + y² = a², the original circle equation alone
  • C (mx+c)² = a², the line equation squared alone
  • D y = mx, leaving out the constant term c altogether

Correct answer: A. x² + y² - a²(mx+c)²/c² = 0

Explanation: Homogenize: x² + y² = a²[(y-mx)/c]² = a²(y-mx)²/c². Rearranging: x²+y² - a²(mx-y)²/c² = 0... The standard result after homogenization.

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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