If a rectangular hyperbola of latus rectum 4 units passing through (0,0) have (2,0) as its one focus, then equation of locus of the other focus is
A
x2+y2=36
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B
x2+y2=4
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C
x2−y2=4
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D
x2−y2=36
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Solution
The correct option is Ax2+y2=36 For a rectangular hyperbola, length of latus rectum =2b2a=2a=2b(∵a=b)
So, 2a=4
Given focus is S(2,0)
Hyperbola passes through the point P(0,0)
Let S′(h,k) be other focal point.
Now, |S′P−SP|=2a ⇒∣∣√h2+k2−2∣∣=4⇒√h2+k2=6⇒h2+k2=36
So, Locus of (h,k) is x2+y2=36