Question:
<p>Circles x<sup>2</sup> + y<sup>2</sup> - 2x - 4y = 0 and x<sup>2</sup> + y<sup>2</sup> - 8y - 4 = 0</p>
<p style="display:inline">cuts each other at two points</p>
<p style="display:inline">touch each other internally</p>
<p style="display:inline">cuts each other</p>
<p style="display:inline">touch each other externally</p>
Step-by-Step Solution
Key Concept: The relative position of two circles is determined by the relationship between the distance between their centers and the sum or difference of their radii.
<p>The centres and radius of given circles are<br />
C<sub>1</sub>(1, 2), C<sub>2</sub>(0, 4), r<sub>1</sub> = <span class="math-tex">$\sqrt{5}$</span> and r<sub>2</sub> = <span class="math-tex">$2\sqrt{5}$</span><br />
Now, C<sub>1</sub>C<sub>2</sub> = <span class="math-tex">$\sqrt{5}$</span> = |r<sub>2</sub> - r<sub>1</sub>|<br />
<span class="math-tex">$\Rightarrow$</span> Circles touch each other internally.</p>
Correct Answer: B