Question
Asked Dec 4, 2019
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Find the standard form for the equation of the hyperbola with foci (0,0) and (8,0) if the conjugate axis is 6 units long.

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Expert Answer

Step 1

Standard form of equation of hyperbola.

Given:
Foci: (0,0)and (8,0).
Conjugate axis: 6 units long.
The standard form of equation of hyperbola:
(x-h)² (y-k)
1
62
Center:(h,k)
a2
Foci:(tc,0)
conjugate axis:=2b.
The distance between two fociis:2c.
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Given: Foci: (0,0)and (8,0). Conjugate axis: 6 units long. The standard form of equation of hyperbola: (x-h)² (y-k) 1 62 Center:(h,k) a2 Foci:(tc,0) conjugate axis:=2b. The distance between two fociis:2c.

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Step 2

Find center:

Take midpoin...

8+0 0+0
Centre :
2
(h,k)=(4,0)
The distance between two foci is,
2c =8-0
2c =8
c= 4
The conjugate axis of hyperbola is,
2b =6
b=3
help_outline

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8+0 0+0 Centre : 2 (h,k)=(4,0) The distance between two foci is, 2c =8-0 2c =8 c= 4 The conjugate axis of hyperbola is, 2b =6 b=3

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Math

Geometry