Let the focus S of the parabola y 2 = 8 x lie on the focal chord P Q of the same parabola. If the length Q S = 3 units, then the ratio of length P Q to the length of the latus rectum of the parabola is

Question

Let the focus S of the parabola y 2 = 8 x lie on the focal chord P Q of the same parabola. If the length Q S = 3 units, then the ratio of length P Q to the length of the latus rectum of the parabola is, 2 5, 4 5, 5 4, 9 8

MARKS App · Accepted Answer

For the focal chord P Q , we know that, P S , 4 , S Q are in H.P. ⇒ 1 P S , 1 4 , 1 3 are in A.P. ⇒ 1 P S = 2 4 - 1 3 = 1 6 ⇒ P S = 6 ⇒ P Q = 6 + 3 = 9 ⇒ P Q length of l a t u s re c t u m = 9 8

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