Straight Lines
Perpendicular Distance and Locus
Grade 11
Question:
<p>Consider a variable line 'L' which passes through the point of intersection 'P' of the lines \(3x + 4y - 12 = 0\) and \(x + 2y - 5 = 0\) meeting the coordinate axes at points A and B. Find the locus of the feet of the perpendicular from the origin on the variable line 'L':</p>
<p>(a) \(2(x^2 + y^2) - 3x - 4y = 0\)</p>
<p>(b) \(2(x^2 + y^2) - 4x - 3y = 0\)</p>
Step-by-Step Solution
Key Concept: Let the foot of perpendicular from origin O to line L be at point M(h,k). Then OM is perpendicular to L, and M lies on L. The line L passes through P and point M. Use the perpendicularity condition and the fact that M lies on a variable line through P.
<p>Not provided in source material.</p>
Correct Answer: A