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For a point P lying on the parabola y² = 4ax, let the line through P and the vertex meet the perpendicular drawn from the focus to the tangent at P at a point R. The locus of R is given by:
- x² + 2y² - ax = 0
- 2x² + y² - 2ax = 0
- 2x² + 2y² - ax = 0
- 2x² + 2y² - ay = 0
Correct answer: 2x² + y² - 2ax = 0
Solution
The correct option describes the locus of point R derived from the geometric properties of the parabola and the relationships between the focus, vertex, and tangent line. This equation captures the necessary conditions that arise from the intersection of the line through point P and the perpendicular from the focus, leading to the specified quadratic form.
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