Question:
<p>ABCD is a square, the length of whose side is a. Taking AB and AD as the coordinate axes, the equation of the circle passing through the vertices of the square is</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> + 2ax + 2ay = 0</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> - 2ax - 2ay = 0</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> - ax - ay = 0</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> + ax + ay = 0</p>
Step-by-Step Solution
Key Concept: The equation of a circle circumscribing a square is determined by using the midpoint of a diagonal as the center and half the diagonal length as the radius.
<html><body><p><img alt="" data-imgur-src="rFZdSrW.png" height="123" src="https://media-mycbseguide.s3.amazonaws.com/images/imgur/1623761627-srvkjx.jpg" width="126"/><br/>
According to the figure, A(0, 0), B(a, 0), C(a, a) and D(0, a).<br/>
The centre is <span class="math-tex">\(\left(\frac{a}{2}, \frac{a}{2}\right)\)</span>.<br/>
The equation of the circle is <span class="math-tex">\(\left(x-\frac{a}{2}\right)^{2}+\left(y-\frac{a}{2}\right)^{2}=\frac{a^{2}}{2}\)</span><br/>
<span class="math-tex">\(\Rightarrow\)</span> x<sup>2</sup> + y<sup>2</sup> - ax - ay = 0</p></body></html>
Correct Answer: C