A set of parallel chords of the parabola $y^{2} = 4 a x$ have their mid points on

any straight line through the vertex

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any straight line through the focus

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a straight line parallel to the axis

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another parabola

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Solution

The correct option is C a straight line parallel to the axis
A set of parallel chords of parabola $y^{2} = 4 x$ have their mid points on:
Locus of mid point of parallel chords is:
$T = S_{1} k y - 2 a (x + h) = k^{2} - 4 a h$
Slope $= m = \frac{2 a}{k}$
$k = \frac{2 a}{m}$
Replace $k \to y$
$y = \frac{2 a}{m}$
Which is straight line parallel to axis.

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A set of parallel chords of the parabola $y^{2} = 4 a x$ have their mid points on

y^{2} = 4 a x

T

T^{'}

{T T}^{'} .

y^{2} = 4 a x

l x + m y + n = 0

P V =

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(ρ)

P V =

(P)

(ρ)

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