Question:
<p>If the coordinates of one end of the diameter of the circle x<sup>2</sup> + y<sup>2</sup> - 8x - 4y + c = 0 are (-3, 2), then the coordinates of other end are</p>
<p style="display:inline">(1, -8)</p>
<p style="display:inline">(6, 2)</p>
<p style="display:inline">(5, 3)</p>
<p style="display:inline">(11, 2)</p>
Step-by-Step Solution
Key Concept: The center of the circle acts as the midpoint of any diameter, allowing the other endpoint to be found by doubling the center coordinates and subtracting the known endpoint.
<p>Here, g = -4, f = -2, x<sub>1</sub> = -3, y<sub>1</sub> = 2<br />
The coordinates of other end<br />
= [-2(-4) + 3, -2(-2) - 2]<br />
= (11, 2)</p>
Correct Answer: D