PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ.
Given that PSQ is a focal chord of the parabola y2 = 8x.
It is also given that SP = 6. We need to find the value of SQ.
Comparing with the standard form of parabola y2 = 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.