The difference of the focal distances of any point on the hyperbola is equal to
(a) length of the conjugate axis
(b) eccentricity
(c) length of the transverse axis
(d) Latus-rectum

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Solution

(c) length of the transverse axis

Let $P (x, y)$ be any point on the hyperbola, and $S, S'$ be the focus with coordinates $(\pm a e, 0)$ .

⇒ $S' P - S P = 2 a$
Thus, the difference of the focal distances of any point on the hyperbola is equal to the length of the transverse axis.

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The difference of the focal distances of any point on the hyperbola is equal to (a) length of the conjugate axis (b) eccentricity (c) length of the transverse axis (d) Latus-rectum

(c) length of the transverse axis Let Px,ybe any point on the hyperbola, and S, S' be the focus with coordinates ±ae,0. ⇒ S'P-SP=2a Thus, the difference of the focal distances of any point on the hyperbola is equal to the length of the transverse axis.

The difference of the focal distances of any point on the hyperbola is equal to
(a) length of the conjugate axis
(b) eccentricity
(c) length of the transverse axis
(d) Latus-rectum

(c) length of the transverse axis

Let $P (x, y)$ be any point on the hyperbola, and $S, S'$ be the focus with coordinates $(\pm a e, 0)$ .

⇒ $S' P - S P = 2 a$
Thus, the difference of the focal distances of any point on the hyperbola is equal to the length of the transverse axis.