If a Chord which is normal to the parabola at one end subtends a right angle at the vertex, then its slope is -

Explanation: 1. Equation of the Normal Let the point be the point on the parabola where the normal is drawn. The equation of the normal to the parabola at point is: Rearranging this in a form suitable for homogenization (to use the vertex condition): Dividing by the constant term: 2. Condition for Subtending a Right Angle at the Vertex The vertex of the parabola is . To find the pair of lines connecting the vertex to the points where the normal intersects the parabola, we homogenize the equation using the line equation: Divide by (assuming ): Rearranging into the standard form of a pair of straight lines : For these lines to be perpendicular (subtend a right angle), the condition is Co-efficient of + Co-efficient of = 0 : Since would mean the normal is the axis of the parabola (which doesn't form a cho

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