The difference of the focal distance of any point on the hyperbola is equal to

length of the conjugale axis

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eccentricity

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length of the transverse axis

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Latus-rectum

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Solution

The correct option is C
length of the transverse axis

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

$\Rightarrow S^{'} P - S P = 2 a$

Thus,the difference of the focla distances of any point on the hyperbola is equal to the length of the transverse axis.

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Similar questions

Q. Assertion(A): The difference of the focal distances of any point on the hyperbola

\frac{x^{2}}{36} - \frac{y^{2}}{9} = 1

is 12.
Reason(R): The difference of the focal distances of any point on the hyperbola is equal to the length of it transverse axis

Q. 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

If the length of the transverse and conjugate axes of a hyperbola be 8 and 6 respectively, then the difference
focal distances of any point of the hyperbola will be

Q. If the length of the transverse and conjugate axes of a hyperbola are

8

and

6

units respectively, then the absolute value of difference of focal distances of any point of the hyperbola is unit.

Q. If the length of the transverse and conjugate axes of a hyperbola are

8

and

6

units respectively, then the absolute value of difference of focal distances of any point of the hyperbola is unit.

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The difference of the focal distance of any point on the hyperbola is equal to

The correct option is C length of the transverse axis Let P(x,y) be any point on the hyperbola, and S,S' be the focus with coordinates (±ae,0) ⇒S′P−SP=2a Thus,the difference of the focla distances of any point on the hyperbola is equal to the length of the transverse axis.