Question:
<p>If the line x + 2by + 7 = 0 is a diameter of the circle x<sup>2</sup> + y<sup>2</sup> - 6x + 2y = 0, then b =</p>
<p style="display:inline">-5</p>
<p style="display:inline">3</p>
<p style="display:inline">-1</p>
<p style="display:inline">5</p>
Step-by-Step Solution
Key Concept: The diameter of a circle always passes through its center, meaning the center's coordinates must satisfy the equation of the diameter line.
<p>Here, the centre of circle (3, -1) must lie on the line x + 2by + 7 = 0.<br />
<span class="math-tex">$\Rightarrow$</span> 3 - 2b + 7 = 0 <span class="math-tex">$\Rightarrow$</span> b = 5</p>
Correct Answer: D