Question:
<p>For the circle x<sup>2</sup> + y<sup>2</sup> + 6x - 8y + 9 = 0, which of the following statement is true?</p>
<p style="display:inline">Circle passes through the point (-2, 3)</p>
<p style="display:inline">Circle touches y-axis</p>
<p style="display:inline">Circle touches x-axis</p>
<p style="display:inline">Circle passes through the point (-3, 4)</p>
Step-by-Step Solution
Key Concept: A circle touches the x-axis if the length of its x-intercept, given by the formula 2√g² - c, is equal to zero.
<p><span class="math-tex">$2 \sqrt{g^{2}-c}=2 \sqrt{9-9}$</span> = 0<br />
Intercept cut on x-axis is zero. Hence circle touches x-axis.</p>
Correct Answer: C