Question:
<p>The radius of the circle passing through the point (6, 2), two of whose diameters are x + y = 6 and x + 2y = 4, is</p>
<p style="display:inline">6</p>
<p style="display:inline">4</p>
<p style="display:inline"><span class="math-tex">\(2 \sqrt{5}\)</span></p>
<p style="display:inline">10</p>
Step-by-Step Solution
Key Concept: The center of a circle is the point of intersection of its diameters, and the radius is the distance from this center to any point on the circumference.
<p>Since, the centre always lies on the diameter.<br />
Solving x + y = 6 and x + 2y = 4,<br />
The co-ordinates of the centre are (8, -2).<br />
<span class="math-tex">$\Rightarrow$</span> Radius <span class="math-tex">$=\sqrt{(8-6)^{2}+(-2-2)^{2}}=\sqrt{20}$</span> <span class="math-tex">$=2 \sqrt{5}$</span></p>
Correct Answer: C