Question:
If the chord joining points \((1,2)\) and \((2,-1)\) on a circle subtends an angle \(\frac{\pi}{4}\) at any point on its circumference, then the equation of such a circle is?
If the chord joining points \((1,2)\) and \((2,-1)\) on a circle subtends an angle \(\frac{\pi}{4}\) at any point on its circumference, then the equation of such a circle is?
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Use angle subtended by chord property and general circle equation passing through chord endpoints.
Updated On: Jun 6, 2025
- \(x^2 + y^2 + 6x - 2y + 5 = 0\)
- \(x^2 + y^2 - 6x - 2y + 5 = 0\)
- \(x^2 + y^2 - 6x + 2y + 5 = 0\)
- \(x^2 + y^2 + 6x + 2y + 5 = 0\)
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The Correct Option is B
Solution and Explanation
Given chord AB between \((1,2)\) and \((2,-1)\).
Circle passes through A and B and every point on circle subtends angle \(\pi/4\) to chord AB.
Using chord length and angle subtended formula, and circle equation general form, the correct equation is
\[
x^2 + y^2 - 6x - 2y + 5 = 0.
\]
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