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

Let points $P (a t_{1}^{2}, 2 a t_{1})$ and $Q (a t_{2}^{2}, 2 a t_{2})$ lie on the parabola $y^{2} = 4 a x$
Here, the points P and Q are variable but slope of the chord PQ, $m_{P Q} = \frac{2}{t_{1} + t_{2}} .$
Now let the mid point of PQ be R(h, k),
$k = \frac{2 a t_{1} + 2 a t_{2}}{2} o r k = a (t_{1} + t_{2}) = \frac{2}{m} \Rightarrow y = \frac{2}{m}$
This is a line parallel to the axis of the parabola

Suggest Corrections

Similar questions

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

x^{2} - y^{2} = a^{2}

y^{2} = 4 a x

y^{2} = 4 a x

l x + m y + n = 0

x^{2} - y^{2} = a^{2}

y^{2} = 4 a x

y^{2} = 4 a x

(α, β)

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