ax2+2bxy+ay2 =c ; c>b>a>0. Minimum distance from origin is....

Dear harshit

compair this with general equatin of second degree

it will be easly shown that this is hyperbola

since curve contain product of XY ,so its axix is not along the co ordinate axis,it is a rotated hyperbola.

since curve is symettric in x and y so it is rotated by 45 degree.

minimum distance can be calculated along the line perpendicular to the directrix. ie y=x

this line cut the parabola at ax² +2bxx+ax² =c

  or                                  x=+-(c/(2a+2b))^1/2

so distance ={x2+x2}^1/2

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                  = (c/(a+b))^1/2

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