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Q.


The auxiliary circle of a hyperbola is defined as:

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a

The auxiliary circle of a hyperbola is a circle with its center on the polar and contains the two vertices.

b

The circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse’s semi major axis.

c

 The auxiliary circle for a hyperbola is a circle with its center on the axis and contains the two vertices.

d

None of these 

answer is C.

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Detailed Solution

The hyperbola's auxiliary circle is the circle which has the same center as the hyperbola while the diameter of the circle is the transverse axis of hyperbola.
The circle contains 2 vertices of the hyperbola as they are end points of transverse axis of the hyperbola.
Here, the auxiliary circle equation for any hyperbola can be given as,
x2+y2=a2
Thus, the definition of auxiliary circle of a hyperbola given in option 3 is correct.
Here, the correct answer is option 3.
 
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