The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as `(-3, -2)` and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The conjugate axis of the hyperbola isA. `4sqrt(11)`B. `2sqrt(11)`C. `4sqrt(22)`D. `2sqrt(22)`

The locus of the foot of perpendicular from my focus of a hyperbola up

1.	The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as `(-3, -2)` and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The conjugate axis of the hyperbola isA. `4sqrt(11)`B. `2sqrt(11)`C. `4sqrt(22)`D. `2sqrt(22)`
Answer» Correct Answer - D Centre `-=(1,2)` Radius of auxiliary circle `=a =sqrt((2-1)^(2)+(5-2)^(2))=sqrt(10)` `2ae=sqrt(8^(2)+8^(2))=8sqrt2 or e=(4)/(sqrt5)` `b^(2)=a^(2)e^(2)-a^(2)=32-10=22` `"or "2b=2sqrt(22)`

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