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# PSQ is a focal chord of the parabola y^{2} = 8x. If SP = 6, then write SQ.

Answer :

Given that PSQ is a focal chord of the parabola y^{2} = 8x.

It is also given that SP = 6. We need to find the value of SQ.

Comparing with the standard form of parabola y^{2} = 4ax

⇒ 4a = 8

⇒ a = 2

We know that the semi - length of the latus - rectum is the harmonic mean of any length of any focal chord.

We know that if a, b, c are in harmonic progression, harmonic mean is given by,

⇒

We know that the semi - length of the latus - rectum is 2a = 4.

⇒

⇒

⇒

⇒ SQ = 3

∴The value of SQ is 3.

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