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Standard XII

Mathematics

Eccentricity of Hyperbola

If the length...

Question

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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Solution

Given $2 a = 8, 2 b = 6$
Now we know that difference of focal distances of any point of the hyperbola is equal to the length of transverse axis $= 2 a = 8$ unit.

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Similar questions

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.

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

S_{1}

and

S_{2}

are the foci of the hyperbola whose transverse axis length is

4

units and conjugate axis length is

6

units,

S_{3}

and

S_{4}

are the foci of the conjugate hyperbola, then the area of the quadrilateral

S_{1} S_{3} S_{2} S_{4}

is sq. units

Q. If

S_{1}

and

S_{2}

are the foci of the hyperbola whose transverse axis length is

4

units and conjugate axis length is

6

units,

S_{3}

and

S_{4}

are the foci of the conjugate hyperbola, then the area of the quadrilateral

S_{1} S_{3} S_{2} S_{4}

is sq. units

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

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Eccentricity of Hyperbola

Standard XII Mathematics

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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.

Given 2a=8, 2b=6 Now we know that difference of focal distances of any point of the hyperbola is equal to the length of transverse axis=2a=8 unit.

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.

Given $2 a = 8, 2 b = 6$
Now we know that difference of focal distances of any point of the hyperbola is equal to the length of transverse axis $= 2 a = 8$ unit.