A hyperbola having the transverse axis of length 2 has the same foci as that of the ellipse 3x2+4y2=12 , then this hyperbola does not pass through which of the following points?
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a
1,−12
b
32,12
c
12,0
d
−32,1
answer is B.
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Detailed Solution
Equation of the given ellipse in the standard form as x24+y3=1 It implies a=2,b=3 and e=1-32=12 Focus =(±1,0) For hyperbola a=12 and foci are same as foci of ellipse, so that a2e2=1⇒e2=2⇒b2=a2=12 Hyperbola x2a22-y2b22=1⇒x2-y2=12Verify the options, option (2) will not satisfy the above equation.
A hyperbola having the transverse axis of length 2 has the same foci as that of the ellipse 3x2+4y2=12 , then this hyperbola does not pass through which of the following points?