Circles
Points on Circle
Grade 11
Question:
<p>Let <em>P</em>(1, 2√2) is a point on circle <em>x</em><sup>2</sup> + <em>y</em><sup>2</sup> = 9. Locate the points on the given circle, which are at 2 units distance from point <em>P</em>.</p>
<p>(a) (-1, 2√2)</p>
<p>(b) (2√2, 1)</p>
<p>(c) (23/9, 10√2/9)</p>
<p>(d) (3, 0)</p>
Step-by-Step Solution
Key Concept: Find points satisfying both the circle equation and the distance constraint from a given point.
<p><strong>Solution:</strong> Points on circle <em>x</em><sup>2</sup> + <em>y</em><sup>2</sup> = 9 that are at distance 2 from P(1, 2√2) can be found by solving the system of the circle equation and the distance formula. Testing the given options and verifying which satisfy both the circle equation and the distance condition yields options (a) and (c).</p>
Correct Answer: a, c