If $(a, b)$ is the mid-point of the chord of the parabola $y^{2} = 4 a x$ passing through the vertex
then which of the following is true?

a = 2 b

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2 a = b

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a^{2} = 2 b

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2 a^{2} = b^{2}

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Solution

The correct option is B $2 a^{2} = b^{2}$
The equation of the chord of the parabola with mid point $(a, b)$ is $S_{1} = S_{11}$
$\Rightarrow y b - 2 a (x + a) = b^{2} - 4 a^{2}$
It passes through vertex $(0, 0)$
Therefore, $2 a^{2} = b^{2}$

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If (a,b) is the mid-point of the chord of the parabola y2=4ax passing through the vertex then which of the following is true?

The correct option is B 2a2=b2 The equation of the chord of the parabola with mid point (a,b) is S1=S11⇒yb−2a(x+a)=b2−4a2It passes through vertex (0,0)Therefore, 2a2=b2

If $(a, b)$ is the mid-point of the chord of the parabola $y^{2} = 4 a x$ passing through the vertex
then which of the following is true?

The correct option is B $2 a^{2} = b^{2}$
The equation of the chord of the parabola with mid point $(a, b)$ is $S_{1} = S_{11}$
$\Rightarrow y b - 2 a (x + a) = b^{2} - 4 a^{2}$
It passes through vertex $(0, 0)$
Therefore, $2 a^{2} = b^{2}$