Straight Lines
General
Grade 11
Question:
A point P(<span class="math-inline">x</span>,<span class="math-inline">y</span>) moves so that the sum of the distance from P to the coordinate axes is equal to the distance from P to the point A(<span class="math-inline">1</span>,<span class="math-inline">1</span>). The equation of the locus of P in the first quadrant is -
x + 1)(y + 1) = 1
x + 1)(y + 1) = 2
x - 1)(y - 1) = 1
x - 1)(y - 1) = 2
Step-by-Step Solution
Key Concept: General
Let A ≡ (a, 0), B = (-a, 0) and P(h, k) so PA ≡ nPB ⇒ (h - a)² + k² = n²[(h + a)² + k²] ⇒ (1 - n²)h² + (1 - n²)k² - 2ah(1 + n² / (1 - n²)) + (1 - n²)a² = 0
Correct Answer: x² + y² - 2ax(1 + n² / (1 - n²)) + a² = 0