Parabola
Locus of points on parabola
Grade 11
Question:
<p>PQ is a double ordinate of the parabola \(y^2 = 4ax\). If the normal at P intersect the line passing through Q and parallel to x-axis at G; then locus of G is a parabola with:</p>
<p>(a) vertex at \((4a, 0)\)</p>
<p>(b) focus at \((5a, 0)\)</p>
<p>(c) directrix as the line \(x - 3a = 0\)</p>
<p>(d) length of latus rectum equal to \(4a\)</p>
Step-by-Step Solution
Key Concept: For a double ordinate PQ on parabola $y^2 = 4ax$, find the locus of point G where the normal at P meets the horizontal line through Q. The resulting locus is another parabola with specific geometric properties.
<p>All options (a), (b), (c), (d) are correct.</p>
Correct Answer: a, b, c, d