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52 lines
2.3 KiB
HTML
52 lines
2.3 KiB
HTML
<div class="book-prose">
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<h2 id="history" class="book-prose__heading">History</h2>
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<p>
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Coordinate methods made circle geometry algebraic: geometric questions about tangency and
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intersection can be solved by equations. This approach grew from analytic geometry.
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</p>
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<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
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<details class="book-question">
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<summary class="book-question__prompt">Find center and radius of \((x+4)^2+(y-1)^2=36\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Center \((-4,1)\), radius \(6\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Write equation of circle with center \((2,-3)\), radius \(7\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \((x-2)^2+(y+3)^2=49\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Is point \((5,1)\) on circle \((x-1)^2+(y-1)^2=16\)?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Yes, \((5-1)^2+(1-1)^2=16\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Convert \(x^2+y^2-6x+4y-12=0\) to standard form.</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \((x-3)^2+(y+2)^2=25\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">A line through tangent point has slope 2. What is slope of radius to that point?</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(-\frac12\).</p>
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</div>
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</details>
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<h2 id="applications" class="book-prose__heading">Applications</h2>
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<ul>
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<li><strong>Engineering:</strong> circular component alignment and tolerance checks.</li>
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<li><strong>Computer graphics:</strong> collision and boundary detection.</li>
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<li><strong>Robotics:</strong> turning path and sensor range modeling.</li>
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</ul>
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<h2 id="references" class="book-prose__heading">References</h2>
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<ul>
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<li>Standard high-school coordinate geometry materials on circles and tangents.</li>
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<li>Analytic geometry references on conic sections (intro level).</li>
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</ul>
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</div>
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