Question:
<p>A pair of perpendicular lines passing through P(1, 4) intersect x-axis at Q and R, then locus of incentre of <span class="math-tex">\(\triangle\)</span>PQR, is:</p>
<p style="display:inline">x<sup>2</sup> - y<sup>2</sup> - 2x + 8y + 17 = 0</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> - 2x - 8y - 17 = 0</p>
<p style="display:inline">x<sup>2</sup> + y<sup>2</sup> + 2x - 8y + 17 = 0</p>
<p style="display:inline">x<sup>2</sup> - y<sup>2</sup> - 2x - 8y + 17 = 0</p>
Step-by-Step Solution
Key Concept: In a right-angled triangle with vertex P and hypotenuse on the x-axis, the incenter I(x,y) forms a square of side y with vertex P, implying the distance PI equals sqrt(2)y.
<p>x<sup>2</sup> - y<sup>2</sup> - 2x - 8y + 17 = 0</p>
Correct Answer: D