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The equation of hyperbola with center at origin and co ordinate axes as its axes, distance between the directrices being 4/√3 and passing through the point (2,1) is? pls explain in detail thanks in advance

The equation of hyperbola with center at origin and co ordinate axes as its axes, distance between the directrices being 4/√3 and passing through the point (2,1) is?
pls explain in detail
thanks in advance

Grade:11

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
2a/e = 4/sqrt(3)..........(i)
Now
 
Hyperbola is of form
 
x²/a² - y²/b² = 1
 
It passes through (2,1)
 
4/a² - 1/b² = 1
 
4b² -a² = a² b²........(ii)
 
Now solve (i) and (ii)
 
You will get values of a² and b²
 
Hence you can get equation of hyperbola

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