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Question

The equation of the hyperbola whose centre is(6,2) one focus is (4,2)  and of eccenticity 2 is


  1. (x6)22(y2)2=1

  2. 3(x6)2(y2)2=3

  3. (x6)23(y2)2=1

  4. 2(x6)2(y2)2=3


Solution

The correct option is B

3(x6)2(y2)2=3


The equation of the hyperbola with centre (x0,y0) is given by

(x0,x0)2a2(y0,y0)b2=1

Focus =(ae+x0,y0)

ae=2

a=1

b2=(2)2a2

b2=(2)2(1)2

b2=3

(x6)21(y2)23=1

3(x6)2(y2)2=3

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