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Question

Let normals drawn to parabola at points P(0,0) and Q(3,1) intersect at (2,1). If PQ is bisected by the axis of the parabola, then

A
Equation of directrix is x+3y+5=0
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B
Slope of axis is 3
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C
Focus is (8,0)
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D
Slope of tangent at vertex is 13
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Solution

The correct option is B Slope of axis is 3
Clearly normals are perpendicular to each other.
So, quadrilateral formed by tangents and normals at given points here forms a rectangle.
axis of the parabola bisects the PQ and tangents drawn to the ends of the chord are perpendicular,
PQ is the latus rectum of the given parabola whose focus is (32,12).
Hence tangents will intersect at (1,2)

directrix is parallel to latus rectum,
Slope of directrix = Slope of tangent at vertex =13 and
Slope of axis =3
So, equation of directrix is y+2=13(x1)
x+3y+5=0

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