hyperbola and cricle

Level pending

If a variable line has its intercepts on the coordinate axes e , e 1 e,e_{1} , where e 2 , e 1 2 \frac {e}{2} , \frac{e_{1}}{2} are the eccentricities of a hyperbola and its conjugate hyperbola respectively, the the line always touches the circle x 2 + y 2 = r 2 x^2+y^2=r^2 . What is the value of r r ?


The answer is 2.

Kirtan Bhatt by kirtan bhatt , 24, India

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1 solution

remember the relation between the eccentricities of hyberbola and its conjugate if e and e' respectively then 1/e^2 + 1/e'^2 =1. now distance from origin is clearly 2 in given problem

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