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Question

The range of k for which |x2+y2x2+y26x8y+25|=k will represent hyperbola is

A
0<k<1
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B
0<k<5
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C
k>5
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D
k>1
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Solution

The correct option is B 0<k<5
|(x0)2+(y0)2(x3)2+(y4)2|=k
Comparing it with |SPSP|=2a
S(0,0) & S(3,4), k=2aSS=2ae=5 ke=5 k=5e
For hyperbola, e>1
0<1e<10<5e<50<k<5

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