Finding the Equation of a Circle

Lecture

• Speaker: Ravi
• Channel: RS Academy
• Main Topic: Finding the equation of a circle passing through points A, B, C.
• Importance: Frequently asked question in exams, repeated many times last year.

Given Points

• A = (1, 2)
• B = (3, -4)
• C = (5, -6)

Steps to Find the Equation

1. Identifying Center and Radius

   • Center postulate (x1, y1)
   • Equidistant radius: SA = SB = SC

2. Solving the Equation

   • Equation SA = SB
     • Squaring on both sides
     • Using the locus formula
   • Substitute point values after squaring

3. Solving the Equations

   • Cancellation and simplification
   • Finding values of y and x by subtracting equations 1 and 2

4. Final Equation

   • Center S = (11, 2)
   • Radius root r² = 100
   • Circle equation: (x - 11)² + (y - 2)² = 100

Tips

• Focus completely for clarity during practice.
• Remember recent usage, formulas.

Study

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