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A rectangular hyperbola of latus rectum ...

A rectangular hyperbola of latus rectum 4 units passes through (0,0) and has (2,0) as its one focus. The equation of locus of the other focus is

A

`x^(2)+y^(2) =36`

B

`x^(2)+y^(2) =4`

C

`x^(2)-y^(2) =4`

D

`x^(2)+y^(2)=9`

Text Solution

Verified by Experts

The correct Answer is:
A
The difference between the focal distance is constant for a hyperbola. For a rectangular hyperbola latus rectum = transverse axis.
One of the foci is `S(2,0)`. Let another focus is `S'(h,k) P(0,0)` is point of the hyperbola
`:. |S'P -SP| = | sqrt(h^(2) +k^(2)) -2| =4`
`rArr sqrt(h^(2)+k^(2)) = 6 rArr h^(2) + k^(2) = 36`
`:.` Locus of (h,k) is `x^(2) + y^(2) = 36`
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